MaplePrimes Questions

Hello everyone, I am facing problem to solve a system of partial differential equations of f, g & q in three variables x,y,t. I have attached the maple file and also a page that i am exploring, in attcahed page I need to find results given in (7) and (8). Maple file is also attached below, please help me to solve this system of PDEs for required results given in (7) and (8). Thanks
 


 

Download PDEs_system_solution.mw

restart

with(PDEtools):

alias(u = u(x, y, t), f = f(x, y, t), g = g(x, y, t), q = q(x, y, t))

u, f, g, q

(1)

eq1 := 24*g*(diff(q, y))*(diff(q, x))^3-12*(diff(q, y))*(diff(q, x))^2*g^2 = 0

24*g*(diff(q, y))*(diff(q, x))^3-12*(diff(q, y))*(diff(q, x))^2*g^2 = 0

(2)

eq2 := 60*g*sigma*(diff(q, y))*(diff(q, x))^3-30*sigma*(diff(q, y))*(diff(q, x))^2*g^2+18*(diff(g, x))*(diff(q, y))*(diff(q, x))^2-15*(diff(q, y))*(diff(q, x))*(diff(g, x))*g+18*g*(diff(q, y))*(diff(q, x))*(diff(q, x, x))-3*(diff(q, y))*g^2*(diff(q, x, x))+6*(diff(g, y))*(diff(q, x))^3+18*g*(diff(q, x))^2*(diff(q, y, x))-9*(diff(g, y))*g*(diff(q, x))^2-3*g^2*(diff(q, x))*(diff(q, y, x)) = 0

60*g*sigma*(diff(q, y))*(diff(q, x))^3-30*sigma*(diff(q, y))*(diff(q, x))^2*g^2+18*(diff(g, x))*(diff(q, y))*(diff(q, x))^2-15*(diff(q, y))*(diff(q, x))*(diff(g, x))*g+18*g*(diff(q, y))*(diff(q, x))*(diff(diff(q, x), x))-3*(diff(q, y))*g^2*(diff(diff(q, x), x))+6*(diff(g, y))*(diff(q, x))^3+18*g*(diff(q, x))^2*(diff(diff(q, x), y))-9*(diff(g, y))*g*(diff(q, x))^2-3*g^2*(diff(q, x))*(diff(diff(q, x), y)) = 0

(3)

eq3 := 36*g*sigma*(diff(q, y))*(diff(q, x))*(diff(q, x, x))-27*sigma*(diff(q, y))*(diff(q, x))*(diff(g, x))*g-3*(diff(q, y))*(diff(g, x))^2+6*(diff(g, y, x))*(diff(q, x))^2-9*(diff(g, y))*(diff(g, x))*(diff(q, x))+2*g*(diff(q, y))*(diff(q, t))+2*g*(diff(q, y))*(diff(q, x, x, x))-6*(diff(f, y))*(diff(q, x))^2*g+12*(diff(g, y))*sigma*(diff(q, x))^3+6*(diff(g, x))*(diff(q, y))*(diff(q, x, x))-3*(diff(q, y, x))*(diff(g, x))*g-3*(diff(q, y))*(diff(g, x, x))*g+6*(diff(q, y))*(diff(g, x, x))*(diff(q, x))-3*(diff(q, x, x))*(diff(g, y))*g-3*g*(diff(q, x))*(diff(g, y, x))+12*(diff(q, x))*(diff(g, x))*(diff(q, y, x))+6*g*(diff(q, y, x))*(diff(q, x, x))+6*(diff(q, x))*g*(diff(q, y, x, x))+6*(diff(g, y))*(diff(q, x))*(diff(q, x, x))-6*sigma*(diff(q, x))*(diff(q, y, x))*g^2+50*g*sigma^2*(diff(q, y))*(diff(q, x))^3-24*sigma^2*(diff(q, y))*(diff(q, x))^2*g^2+36*(diff(g, x))*sigma*(diff(q, y))*(diff(q, x))^2-15*(diff(q, x))^2*sigma*(diff(g, y))*g-6*(diff(f, x))*(diff(q, y))*(diff(q, x))*g-6*sigma*(diff(q, y))*(diff(q, x, x))*g^2+36*g*sigma*(diff(q, x))^2*(diff(q, y, x)) = 0

50*g*sigma^2*(diff(q, y))*(diff(q, x))^3-24*sigma^2*(diff(q, y))*(diff(q, x))^2*g^2+36*(diff(g, x))*sigma*(diff(q, y))*(diff(q, x))^2-15*(diff(q, x))^2*sigma*(diff(g, y))*g-6*(diff(f, x))*(diff(q, y))*(diff(q, x))*g-6*sigma*(diff(q, x))*(diff(diff(q, x), y))*g^2-6*sigma*(diff(q, y))*(diff(diff(q, x), x))*g^2+36*g*sigma*(diff(q, x))^2*(diff(diff(q, x), y))-3*(diff(q, y))*(diff(g, x))^2+6*(diff(diff(g, x), y))*(diff(q, x))^2+6*(diff(g, y))*(diff(q, x))*(diff(diff(q, x), x))+6*(diff(g, x))*(diff(q, y))*(diff(diff(q, x), x))-3*(diff(diff(q, x), y))*(diff(g, x))*g-3*(diff(q, y))*(diff(diff(g, x), x))*g+6*(diff(q, y))*(diff(diff(g, x), x))*(diff(q, x))-3*(diff(diff(q, x), x))*(diff(g, y))*g-3*g*(diff(q, x))*(diff(diff(g, x), y))+12*(diff(q, x))*(diff(g, x))*(diff(diff(q, x), y))+6*g*(diff(diff(q, x), y))*(diff(diff(q, x), x))+6*(diff(q, x))*g*(diff(diff(diff(q, x), x), y))+2*g*(diff(q, y))*(diff(diff(diff(q, x), x), x))+2*g*(diff(q, y))*(diff(q, t))+12*(diff(g, y))*sigma*(diff(q, x))^3-9*(diff(g, y))*(diff(g, x))*(diff(q, x))-6*(diff(f, y))*(diff(q, x))^2*g-27*sigma*(diff(q, y))*(diff(q, x))*(diff(g, x))*g+36*g*sigma*(diff(q, y))*(diff(q, x))*(diff(diff(q, x), x)) = 0

(4)

eq4 := -3*g*(diff(f, y))*(diff(q, x, x))-3*(diff(q, y))*g*(diff(f, x, x))-3*g*(diff(q, x))*(diff(f, y, x))-3*g*(diff(q, y, x))*(diff(f, x))+15*g*sigma^3*(diff(q, y))*(diff(q, x))^3-6*sigma^3*(diff(q, y))*(diff(q, x))^2*g^2+21*(diff(g, x))*sigma^2*(diff(q, y))*(diff(q, x))^2-6*(diff(q, x))^2*sigma^2*(diff(g, y))*g-9*(diff(f, y))*(diff(q, x))^2*sigma*g+3*g*sigma*(diff(q, y))*(diff(q, t))-9*sigma*(diff(q, x))*(diff(g, x))*(diff(g, y))+9*(diff(g, y, x))*sigma*(diff(q, x))^2+7*(diff(g, y))*sigma^2*(diff(q, x))^3-3*sigma*(diff(q, y))*(diff(g, x))^2-6*(diff(g, x))*(diff(q, x))*(diff(f, y))-3*(diff(q, y))*(diff(g, x))*(diff(f, x))-3*(diff(g, y))*(diff(q, x))*(diff(f, x))-3*(diff(g, y, x))*(diff(g, x))-3*(diff(g, x, x))*(diff(g, y))+g*(diff(q, y, t))+9*g*sigma*(diff(q, y, x))*(diff(q, x, x))-3*sigma*(diff(q, x, x))*(diff(g, y))*g+9*sigma*(diff(q, x))*g*(diff(q, y, x, x))-3*sigma*(diff(q, y, x))*(diff(g, x))*g-3*sigma*(diff(q, x))*(diff(g, y, x))*g+9*(diff(g, y))*sigma*(diff(q, x))*(diff(q, x, x))+9*(diff(g, x))*sigma*(diff(q, y))*(diff(q, x, x))+3*g*sigma*(diff(q, y))*(diff(q, x, x, x))+18*sigma*(diff(q, x))*(diff(g, x))*(diff(q, y, x))+21*g*sigma^2*(diff(q, x))^2*(diff(q, y, x))-3*sigma^2*(diff(q, x))*(diff(q, y, x))*g^2+9*sigma*(diff(q, y))*(diff(g, x, x))*(diff(q, x))-3*sigma*(diff(q, y))*(diff(g, x, x))*g-3*sigma^2*(diff(q, y))*(diff(q, x, x))*g^2+21*g*sigma^2*(diff(q, y))*(diff(q, x))*(diff(q, x, x))-9*(diff(f, x))*(diff(q, y))*(diff(q, x))*sigma*g-12*sigma^2*(diff(q, y))*(diff(q, x))*(diff(g, x))*g+(diff(q, y))*(diff(g, t))+(diff(g, y))*(diff(q, t))+3*(diff(g, x, x))*(diff(q, y, x))+(diff(q, y))*(diff(g, x, x, x))+3*(diff(q, x))*(diff(g, y, x, x))+(diff(q, y, x, x, x))*g+3*(diff(g, x))*(diff(q, y, x, x))+(diff(g, y))*(diff(q, x, x, x))+3*(diff(g, y, x))*(diff(q, x, x)) = 0

7*(diff(g, y))*sigma^2*(diff(q, x))^3-3*sigma*(diff(q, y))*(diff(g, x))^2-6*(diff(g, x))*(diff(q, x))*(diff(f, y))-3*(diff(q, y))*(diff(g, x))*(diff(f, x))-3*(diff(g, y))*(diff(q, x))*(diff(f, x))-3*(diff(q, y))*g*(diff(diff(f, x), x))-3*g*(diff(q, x))*(diff(diff(f, x), y))-3*g*(diff(f, y))*(diff(diff(q, x), x))-3*g*(diff(diff(q, x), y))*(diff(f, x))+9*(diff(diff(g, x), y))*sigma*(diff(q, x))^2+15*g*sigma^3*(diff(q, y))*(diff(q, x))^3-6*sigma^3*(diff(q, y))*(diff(q, x))^2*g^2+21*(diff(g, x))*sigma^2*(diff(q, y))*(diff(q, x))^2-6*(diff(q, x))^2*sigma^2*(diff(g, y))*g-9*(diff(f, y))*(diff(q, x))^2*sigma*g+3*g*sigma*(diff(q, y))*(diff(q, t))-9*sigma*(diff(q, x))*(diff(g, x))*(diff(g, y))+9*g*sigma*(diff(diff(q, x), y))*(diff(diff(q, x), x))-3*sigma*(diff(diff(q, x), x))*(diff(g, y))*g+9*sigma*(diff(q, x))*g*(diff(diff(diff(q, x), x), y))-3*sigma*(diff(diff(q, x), y))*(diff(g, x))*g-3*sigma*(diff(q, x))*(diff(diff(g, x), y))*g+9*(diff(g, y))*sigma*(diff(q, x))*(diff(diff(q, x), x))+9*(diff(g, x))*sigma*(diff(q, y))*(diff(diff(q, x), x))+3*g*sigma*(diff(q, y))*(diff(diff(diff(q, x), x), x))+18*sigma*(diff(q, x))*(diff(g, x))*(diff(diff(q, x), y))+21*g*sigma^2*(diff(q, x))^2*(diff(diff(q, x), y))-3*sigma^2*(diff(q, x))*(diff(diff(q, x), y))*g^2+9*sigma*(diff(q, y))*(diff(diff(g, x), x))*(diff(q, x))-3*sigma*(diff(q, y))*(diff(diff(g, x), x))*g-3*sigma^2*(diff(q, y))*(diff(diff(q, x), x))*g^2-9*(diff(f, x))*(diff(q, y))*(diff(q, x))*sigma*g-12*sigma^2*(diff(q, y))*(diff(q, x))*(diff(g, x))*g+21*g*sigma^2*(diff(q, y))*(diff(q, x))*(diff(diff(q, x), x))+(diff(q, y))*(diff(g, t))+(diff(g, y))*(diff(q, t))-3*(diff(diff(g, x), y))*(diff(g, x))-3*(diff(diff(g, x), x))*(diff(g, y))+g*(diff(diff(q, t), y))+3*(diff(diff(g, x), x))*(diff(diff(q, x), y))+(diff(q, y))*(diff(diff(diff(g, x), x), x))+3*(diff(q, x))*(diff(diff(diff(g, x), x), y))+(diff(diff(diff(diff(q, x), x), x), y))*g+3*(diff(g, x))*(diff(diff(diff(q, x), x), y))+(diff(g, y))*(diff(diff(diff(q, x), x), x))+3*(diff(diff(g, x), y))*(diff(diff(q, x), x)) = 0

(5)

eq5 := (diff(g, y))*sigma*(diff(q, t))+(diff(g, t))*sigma*(diff(q, y))+(diff(g, y))*sigma^3*(diff(q, x))^3+3*(diff(g, x))*sigma^3*(diff(q, y))*(diff(q, x))^2+g*sigma^2*(diff(q, y))*(diff(q, t))+g*sigma^4*(diff(q, y))*(diff(q, x))^3-3*(diff(f, x))*sigma*(diff(q, y))*(diff(g, x))-3*(diff(f, x))*sigma*(diff(q, x))*(diff(g, y))-6*(diff(f, y))*sigma*(diff(q, x))*(diff(g, x))+3*g*sigma^3*(diff(q, x))^2*(diff(q, y, x))+g*sigma^2*(diff(q, y))*(diff(q, x, x, x))-3*(diff(f, x))*sigma*(diff(q, y, x))*g-3*(diff(f, y))*sigma*(diff(q, x, x))*g-3*g*sigma*(diff(q, y))*(diff(f, x, x))-3*sigma*(diff(q, x))*g*(diff(f, y, x))+3*(diff(g, x, x))*sigma^2*(diff(q, y))*(diff(q, x))+6*(diff(g, x))*sigma^2*(diff(q, x))*(diff(q, y, x))+diff(g, y, t)-3*(diff(f, x))*(diff(q, y))*(diff(q, x))*sigma^2*g+3*g*sigma^3*(diff(q, y))*(diff(q, x))*(diff(q, x, x))+3*g*sigma^2*(diff(q, x))*(diff(q, y, x, x))-3*(diff(f, y))*(diff(q, x))^2*sigma^2*g+3*(diff(g, y))*sigma^2*(diff(q, x))*(diff(q, x, x))+3*g*sigma^2*(diff(q, y, x))*(diff(q, x, x))+3*(diff(g, x))*sigma^2*(diff(q, y))*(diff(q, x, x))-3*(diff(g, y))*(diff(f, x, x))-3*(diff(f, y))*(diff(g, x, x))-3*(diff(g, x))*(diff(f, y, x))-3*(diff(f, x))*(diff(g, y, x))+diff(g, y, x, x, x)+3*(diff(g, y, x))*sigma^2*(diff(q, x))^2+3*(diff(g, x, x))*sigma*(diff(q, y, x))+3*(diff(g, y, x, x))*sigma*(diff(q, x))+(diff(g, x, x, x))*sigma*(diff(q, y))+g*sigma*(diff(q, y, t))+3*(diff(g, x))*sigma*(diff(q, y, x, x))+3*(diff(g, y, x))*sigma*(diff(q, x, x))+g*sigma*(diff(q, y, x, x, x))+(diff(g, y))*sigma*(diff(q, x, x, x)) = 0

(diff(g, t))*sigma*(diff(q, y))+(diff(g, y))*sigma^3*(diff(q, x))^3+(diff(g, y))*sigma*(diff(q, t))+3*(diff(diff(g, x), y))*sigma^2*(diff(q, x))^2+3*(diff(diff(g, x), x))*sigma*(diff(diff(q, x), y))+3*(diff(diff(diff(g, x), x), y))*sigma*(diff(q, x))+(diff(diff(diff(g, x), x), x))*sigma*(diff(q, y))+g*sigma*(diff(diff(q, t), y))+3*(diff(g, x))*sigma*(diff(diff(diff(q, x), x), y))+3*(diff(diff(g, x), y))*sigma*(diff(diff(q, x), x))+g*sigma*(diff(diff(diff(diff(q, x), x), x), y))+(diff(g, y))*sigma*(diff(diff(diff(q, x), x), x))-3*(diff(f, x))*(diff(q, y))*(diff(q, x))*sigma^2*g+3*g*sigma^3*(diff(q, y))*(diff(q, x))*(diff(diff(q, x), x))-3*(diff(f, y))*(diff(q, x))^2*sigma^2*g+6*(diff(g, x))*sigma^2*(diff(q, x))*(diff(diff(q, x), y))+3*g*sigma^2*(diff(q, x))*(diff(diff(diff(q, x), x), y))+3*(diff(g, y))*sigma^2*(diff(q, x))*(diff(diff(q, x), x))+3*g*sigma^2*(diff(diff(q, x), y))*(diff(diff(q, x), x))+3*(diff(g, x))*sigma^2*(diff(q, y))*(diff(diff(q, x), x))+3*g*sigma^3*(diff(q, x))^2*(diff(diff(q, x), y))+g*sigma^2*(diff(q, y))*(diff(diff(diff(q, x), x), x))-3*(diff(f, x))*sigma*(diff(diff(q, x), y))*g-3*(diff(f, y))*sigma*(diff(diff(q, x), x))*g-3*g*sigma*(diff(q, y))*(diff(diff(f, x), x))-3*sigma*(diff(q, x))*g*(diff(diff(f, x), y))+3*(diff(diff(g, x), x))*sigma^2*(diff(q, y))*(diff(q, x))+3*(diff(g, x))*sigma^3*(diff(q, y))*(diff(q, x))^2+g*sigma^2*(diff(q, y))*(diff(q, t))+g*sigma^4*(diff(q, y))*(diff(q, x))^3-3*(diff(f, x))*sigma*(diff(q, y))*(diff(g, x))-3*(diff(f, x))*sigma*(diff(q, x))*(diff(g, y))-6*(diff(f, y))*sigma*(diff(q, x))*(diff(g, x))+diff(diff(g, t), y)+diff(diff(diff(diff(g, x), x), x), y)-3*(diff(g, y))*(diff(diff(f, x), x))-3*(diff(f, y))*(diff(diff(g, x), x))-3*(diff(g, x))*(diff(diff(f, x), y))-3*(diff(f, x))*(diff(diff(g, x), y)) = 0

(6)

eq6 := -3*(diff(f, x))*(diff(f, y, x))-3*(diff(f, y))*(diff(f, x, x))+diff(f, y, x, x, x)+diff(f, y, t) = 0

-3*(diff(f, x))*(diff(diff(f, x), y))-3*(diff(f, y))*(diff(diff(f, x), x))+diff(diff(diff(diff(f, x), x), x), y)+diff(diff(f, t), y) = 0

(7)

pdsolve({eq1, eq2, eq3, eq4, eq5, eq6}, {f, g, q})

``

Download PDEs_system_solution.mw

Can maple simplify a Combined Inequality? At best it outputs imho a more complicated solution.

Thanks in Advance.

sl10 := -1 <= (3-5*x)*(1/2) and (3-5*x)*(1/2) <= 9

0 <= 5/2-(5/2)*x and -(5/2)*x <= 15/2

(1)

The output should be:

 

-3 <= x and x <= 1


Download Combined_Inequality.mw

This is a very serious problem. Maple 2024.2 on windows 10.

I noticed, may be starting 2-3 weeks now, that sometimes when I do File->Open , and the Open dialogue opens, I am not able to use the mouse to select the .mw file I want to open. 

Can not even close the dialogue by clicking X. Even clickiing on cancel does nothing.  Basically the mouse seems not doing anything.

Only way is to type using the keyboard the file name. Eveything else does not work.

Not only that, the mouse is trapped in the dialogue.

I can't even get it out of Maple to go to another application. AT first, I had to do CTRL-ALT-DEL to get out and use the task manager to kill Maple. Then later I found if I type the file name I can get out.

Here is a movie.  

I do not understand what is causing this. This only happens in Maple for me. Neven seen anything like this before.

Any suggestions what to look for?

I just remembered. 2-3 weeks ago, I closed the left panel. As you see above.

I just tried now, and expanded it again, and guess what, the mouse seems to be working now!

Can someone conform this?  Here is a movie with the panel expanded again:

You see, the mouse now works and can select files.

When I minimize the left panel, the mouse sometimes stops working in file dialogue.

Here is another movie showing this problem much more clearly.

When closing the left panel, the open file dialogue stops working (mouse not working), and when expanding it again, it starts to work!

This can not be a feature right? it must be a bug in the Java interface?

Here's a puzzle for geometry lovers. It has a very short manual solution, but it's not that easy to find. Of course, you can solve it in Maple using coordinates. You need to find the radius of these two identical circles.

I am using the tab key to complete commands. Often I have to add a module to the command. On my keyboard typing ":-" is slow (for me) and interrupts the flow. I was wondering whether there is not a undocumented key or shortcut to insert ":-".

(I tried a second time hitting tab but this did not do anything. Would this be a good way to speed up typing?)

I wanted to derive the q(w) term in the following expression to get ∂ f/∂q(w), but I got an error

every thing is correct but i dont know why my PDE is not be zero, i did by another way is satidy but i change whole equation by sabstitutiin then i did ode test is satisfy by putting case in equation and solution with condition but when i want to use pdetest  test in pde is not satisfy ?

restart

_local(gamma)

with(PDEtools)

NULL

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

(1)

declare(Omega(x, t)); declare(U(xi)); declare(V(xi)); declare(Theta(x, t))

Omega(x, t)*`will now be displayed as`*Omega

 

U(xi)*`will now be displayed as`*U

 

V(xi)*`will now be displayed as`*V

 

Theta(x, t)*`will now be displayed as`*Theta

(2)

xi := -t*tau+x

-t*tau+x

(3)

NULL

NULL

lambda := -tau/c; epsilon := -tau/c; delta := (2*c^2-gamma*tau)/(gamma-2*tau)

-tau/c

 

-tau/c

 

(2*c^2-gamma*tau)/(gamma-2*tau)

(4)

NULL

case1 := [c = RootOf(-gamma^3*tau+2*_Z^2+2*gamma*tau-4*tau^2)/gamma, A[0] = 0, A[1] = RootOf(_Z^2*gamma+2*tau), B[1] = 0]

[c = RootOf(-gamma^3*tau+2*_Z^2+2*gamma*tau-4*tau^2)/gamma, A[0] = 0, A[1] = RootOf(_Z^2*gamma+2*tau), B[1] = 0]

(5)

K := Omega(x, t) = RootOf(_Z^2*gamma+2*tau)*tanh(xi)*exp(I*gamma*(delta*t+x))

Omega(x, t) = -RootOf(_Z^2*gamma+2*tau)*tanh(t*tau-x)*exp(I*gamma*((2*c^2-gamma*tau)*t/(gamma-2*tau)+x))

(6)

NULL

pde1 := I*(diff(Omega(x, t), `$`(t, 2))-c^2*(diff(Omega(x, t), `$`(x, 2))))+diff(U(-t*tau+x)^2*Omega(x, t), t)-lambda*c*(diff(U(-t*tau+x)^2*Omega(x, t), x))+(1/2)*(diff(Omega(x, t), `$`(x, 2), t))-(1/2)*epsilon*c*(diff(Omega(x, t), `$`(x, 3))) = 0

I*(diff(diff(Omega(x, t), t), t)-c^2*(diff(diff(Omega(x, t), x), x)))-2*U(-t*tau+x)*Omega(x, t)*(D(U))(-t*tau+x)*tau+U(-t*tau+x)^2*(diff(Omega(x, t), t))+tau*(2*U(-t*tau+x)*Omega(x, t)*(D(U))(-t*tau+x)+U(-t*tau+x)^2*(diff(Omega(x, t), x)))+(1/2)*(diff(diff(diff(Omega(x, t), t), x), x))+(1/2)*tau*(diff(diff(diff(Omega(x, t), x), x), x)) = 0

(7)

NULL

subs(case1, pde1)

I*(diff(diff(Omega(x, t), t), t)-RootOf(-gamma^3*tau+2*_Z^2+2*gamma*tau-4*tau^2)^2*(diff(diff(Omega(x, t), x), x))/gamma^2)-2*U(-t*tau+x)*Omega(x, t)*(D(U))(-t*tau+x)*tau+U(-t*tau+x)^2*(diff(Omega(x, t), t))+tau*(2*U(-t*tau+x)*Omega(x, t)*(D(U))(-t*tau+x)+U(-t*tau+x)^2*(diff(Omega(x, t), x)))+(1/2)*(diff(diff(diff(Omega(x, t), t), x), x))+(1/2)*tau*(diff(diff(diff(Omega(x, t), x), x), x)) = 0

(8)

T := simplify(I*(diff(diff(Omega(x, t), t), t)-RootOf(-gamma^3*tau+2*_Z^2+2*gamma*tau-4*tau^2)^2*(diff(diff(Omega(x, t), x), x))/gamma^2)-2*U(-t*tau+x)*Omega(x, t)*(D(U))(-t*tau+x)*tau+U(-t*tau+x)^2*(diff(Omega(x, t), t))+tau*(2*U(-t*tau+x)*Omega(x, t)*(D(U))(-t*tau+x)+U(-t*tau+x)^2*(diff(Omega(x, t), x)))+(1/2)*(diff(diff(diff(Omega(x, t), t), x), x))+(1/2)*tau*(diff(diff(diff(Omega(x, t), x), x), x)) = 0)

(1/2)*(2*gamma^2*(tau*(diff(Omega(x, t), x))+diff(Omega(x, t), t))*U(-t*tau+x)^2+(diff(diff(diff(Omega(x, t), t), x), x))*gamma^2+tau*(diff(diff(diff(Omega(x, t), x), x), x))*gamma^2-(4*I)*((1/4)*gamma^3+tau-(1/2)*gamma)*tau*(diff(diff(Omega(x, t), x), x))+(2*I)*(diff(diff(Omega(x, t), t), t))*gamma^2)/gamma^2 = 0

(9)

pdetest(K, T)

-(1/2)*2^(1/2)*(-tau/gamma)^(1/2)*(-32*gamma^4*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+16*gamma^5*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-8*gamma^6*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+32*gamma^5*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-32*gamma^4*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+16*gamma^4*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-96*gamma^3*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+192*gamma^2*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-128*tau^4*gamma*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+16*gamma^4*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-96*gamma^3*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+192*gamma^2*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-128*tau^4*gamma*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+16*gamma^5*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-8*gamma^6*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(4*I)*U(-t*tau+x)^2*gamma^4*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))+(4*I)*U(-t*tau+x)^2*gamma^4*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))-(8*I)*U(-t*tau+x)^2*gamma^3*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))-(12*I)*gamma^5*c^2*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))+(4*I)*U(-t*tau+x)^2*gamma^4*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))-(4*I)*U(-t*tau+x)^2*gamma^4*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))+(8*I)*U(-t*tau+x)^2*gamma^3*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))+(12*I)*gamma^5*c^2*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))+(4*I)*U(-t*tau+x)^2*gamma^4*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(4*I)*U(-t*tau+x)^2*gamma^4*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+(8*I)*U(-t*tau+x)^2*gamma^3*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+(12*I)*gamma^5*c^2*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(4*I)*U(-t*tau+x)^2*gamma^4*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+(4*I)*U(-t*tau+x)^2*gamma^4*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-(8*I)*U(-t*tau+x)^2*gamma^3*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-(12*I)*gamma^5*c^2*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+(32*I)*gamma^3*c^2*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(32*I)*gamma^3*c^2*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-64*gamma^4*c^2*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+64*gamma^3*tau^2*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+I*tau*gamma^7*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-64*gamma^4*c^2*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+64*gamma^3*tau^2*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+I*tau*gamma^7*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))+(192*I)*tau^3*gamma*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-(8*I)*c^4*gamma^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(2*I)*c^2*gamma^6*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(4*I)*tau^2*gamma^6*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+(8*I)*c^4*gamma^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+(2*I)*c^2*gamma^6*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-I*tau*gamma^7*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+(4*I)*tau^2*gamma^6*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-(16*I)*gamma^4*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+(6*I)*tau*gamma^5*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(20*I)*gamma^4*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+(40*I)*gamma^3*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(48*I)*gamma^2*tau^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+(16*I)*gamma^4*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-(6*I)*tau*gamma^5*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+(20*I)*gamma^4*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-(40*I)*gamma^3*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+(48*I)*gamma^2*tau^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-(16*I)*gamma^3*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+(96*I)*gamma^2*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(192*I)*tau^3*gamma*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+(16*I)*gamma^3*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-(96*I)*gamma^2*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-I*tau*gamma^7*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))+(4*I)*tau^2*gamma^6*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))-(8*I)*c^4*gamma^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))-(2*I)*c^2*gamma^6*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))-(4*I)*tau^2*gamma^6*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))+(8*I)*c^4*gamma^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))+(2*I)*tau*gamma^5*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))-(12*I)*gamma^4*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))+(24*I)*gamma^3*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))-(16*I)*gamma^2*tau^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))-(2*I)*tau*gamma^5*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))+(12*I)*gamma^4*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))-(24*I)*gamma^3*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))+(16*I)*gamma^2*tau^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))+(2*I)*c^2*gamma^6*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))+32*gamma^5*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+(128*I)*tau^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(128*I)*tau^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-(8*I)*tau*c^2*U(-t*tau+x)^2*gamma^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))+(8*I)*tau*c^2*U(-t*tau+x)^2*gamma^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))-(8*I)*tau*c^2*U(-t*tau+x)^2*gamma^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+(8*I)*tau*c^2*U(-t*tau+x)^2*gamma^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau)))/(gamma^2*(gamma-2*tau)^2*(exp(2*t*tau)+exp(2*x))^3)

(10)

simplify(-(1/2)*2^(1/2)*(-tau/gamma)^(1/2)*((8*I)*tau*c^2*U(-t*tau+x)^2*gamma^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))+(8*I)*tau*c^2*U(-t*tau+x)^2*gamma^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-(8*I)*tau*c^2*U(-t*tau+x)^2*gamma^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))-(8*I)*tau*c^2*U(-t*tau+x)^2*gamma^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(128*I)*tau^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+32*gamma^5*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+192*gamma^2*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-128*tau^4*gamma*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+16*gamma^5*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-8*gamma^6*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+32*gamma^5*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-32*gamma^4*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+16*gamma^4*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-96*gamma^3*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+192*gamma^2*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-128*tau^4*gamma*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+16*gamma^4*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-96*gamma^3*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+(128*I)*tau^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-32*gamma^4*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+16*gamma^5*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-8*gamma^6*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-(32*I)*gamma^3*c^2*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+(4*I)*U(-t*tau+x)^2*gamma^4*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))+(4*I)*U(-t*tau+x)^2*gamma^4*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))+(8*I)*U(-t*tau+x)^2*gamma^3*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))+(12*I)*gamma^5*c^2*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))+(4*I)*U(-t*tau+x)^2*gamma^4*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+(8*I)*U(-t*tau+x)^2*gamma^3*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+(12*I)*gamma^5*c^2*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+(4*I)*U(-t*tau+x)^2*gamma^4*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+(32*I)*gamma^3*c^2*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(4*I)*U(-t*tau+x)^2*gamma^4*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))-(8*I)*U(-t*tau+x)^2*gamma^3*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))-(12*I)*gamma^5*c^2*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))-(4*I)*U(-t*tau+x)^2*gamma^4*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))-(4*I)*U(-t*tau+x)^2*gamma^4*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(4*I)*U(-t*tau+x)^2*gamma^4*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-(8*I)*U(-t*tau+x)^2*gamma^3*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-(12*I)*gamma^5*c^2*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-(8*I)*c^4*gamma^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(2*I)*c^2*gamma^6*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(4*I)*tau^2*gamma^6*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-I*tau*gamma^7*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-(16*I)*gamma^4*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(20*I)*gamma^4*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(48*I)*gamma^2*tau^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(6*I)*tau*gamma^5*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-(40*I)*gamma^3*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-(16*I)*gamma^3*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(192*I)*tau^3*gamma*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))-(96*I)*gamma^2*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-I*tau*gamma^7*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))-(8*I)*c^4*gamma^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))-(2*I)*c^2*gamma^6*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))-(4*I)*tau^2*gamma^6*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))-(12*I)*gamma^4*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))-(16*I)*gamma^2*tau^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))-(2*I)*tau*gamma^5*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))-(24*I)*gamma^3*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))-64*gamma^4*c^2*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+64*gamma^3*tau^2*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))-64*gamma^4*c^2*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+64*gamma^3*tau^2*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+(8*I)*c^4*gamma^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))+(2*I)*tau*gamma^5*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))+(24*I)*gamma^3*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))+(12*I)*gamma^4*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))+(16*I)*gamma^2*tau^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))+(2*I)*c^2*gamma^6*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))+(48*I)*gamma^2*tau^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+(96*I)*gamma^2*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+(16*I)*gamma^3*tau*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+(4*I)*tau^2*gamma^6*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*x*gamma-12*x*tau)/(gamma-2*tau))+(2*I)*c^2*gamma^6*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+(4*I)*tau^2*gamma^6*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+(6*I)*tau*gamma^5*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+(40*I)*gamma^3*tau^3*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+(16*I)*gamma^4*c^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+(20*I)*gamma^4*tau^2*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+I*tau*gamma^7*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+4*gamma*t*tau-8*t*tau^2+2*x*gamma-4*x*tau)/(gamma-2*tau))+I*tau*gamma^7*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+6*gamma*t*tau-12*t*tau^2)/(gamma-2*tau))+(192*I)*tau^3*gamma*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau))+(8*I)*c^4*gamma^4*exp(((2*I)*gamma*c^2*t-I*gamma^2*t*tau+I*x*gamma^2-(2*I)*gamma*x*tau+2*gamma*t*tau-4*t*tau^2+4*x*gamma-8*x*tau)/(gamma-2*tau)))/(gamma^2*(gamma-2*tau)^2*(exp(2*tau*t)+exp(2*x))^3))

-(-tau/gamma)^(1/2)*((I*gamma^3*(-(1/2)*gamma+tau)*(c-tau)*(c+tau)*U(-t*tau+x)^2-((1/8)*I)*tau*gamma^7+(((1/4)*I)*c^2+((1/2)*I)*tau^2-tau)*gamma^6+(4*tau^2+(-((3/2)*I)*c^2-(3/4)*I)*tau+2*c^2)*gamma^5+(-4*tau^3+((5/2)*I)*tau^2+(-8*c^2+2)*tau+I*(c^2+2)*c^2)*gamma^4-4*(((5/4)*I)*tau^2+(-2*c^2+3)*tau+I*c^2-(1/2)*I)*tau*gamma^3+6*(I*tau^2-2*I+4*tau)*tau^2*gamma^2+((24*I)*tau^3-16*tau^4)*gamma-(16*I)*tau^4)*exp((I*(t*tau-x)*gamma^2+2*((I*x-t)*tau-I*c^2*t-2*x)*gamma+4*t*tau^2+8*x*tau)/(-gamma+2*tau))+(-I*gamma^3*(-(1/2)*gamma+tau)*(c-tau)*(c+tau)*U(-t*tau+x)^2+((1/8)*I)*tau*gamma^7+(-((1/4)*I)*c^2-((1/2)*I)*tau^2-tau)*gamma^6+(4*tau^2+(((3/2)*I)*c^2+(3/4)*I)*tau+2*c^2)*gamma^5+(-4*tau^3-((5/2)*I)*tau^2+(-8*c^2+2)*tau-I*(c^2+2)*c^2)*gamma^4+4*(((5/4)*I)*tau^2+tau*(2*c^2-3)+I*c^2-(1/2)*I)*tau*gamma^3-6*(I*tau^2-2*I-4*tau)*tau^2*gamma^2+(-(24*I)*tau^3-16*tau^4)*gamma+(16*I)*tau^4)*exp((I*(t*tau-x)*gamma^2+2*((I*x-2*t)*tau-I*c^2*t-x)*gamma+8*t*tau^2+4*x*tau)/(-gamma+2*tau))+I*gamma^2*(exp((I*(t*tau-x)*gamma^2+2*(-I*c^2*t+I*x*tau-3*x)*gamma+12*x*tau)/(-gamma+2*tau))-exp((I*(t*tau-x)*gamma^2+2*((I*x-3*t)*tau-I*c^2*t)*gamma+12*t*tau^2)/(-gamma+2*tau)))*(gamma*(-(1/2)*gamma+tau)*(c-tau)*(c+tau)*U(-t*tau+x)^2-(1/8)*tau*gamma^5+((1/4)*c^2+(1/2)*tau^2)*gamma^4+tau*(-(3/2)*c^2+1/4)*gamma^3+(c^4-(3/2)*tau^2)*gamma^2+3*tau^3*gamma-2*tau^4))*2^(1/2)/(gamma^2*(exp(2*t*tau)+exp(2*x))^3*(-(1/2)*gamma+tau)^2)

(11)
 

 

Download pdetest.mw

Is there something one can do to make Maple give same result each time? It seems all random.

Calling odetest sometimes gives internal error. 

            Error, (in trig/normal/sincosargs) too many levels of recursion

But it is random when and how it happens. Worksheet below shows that sometimes when adding infolevel[odetest]:=5; make the error go away. sometimes trying 2 or 3 times also makes the error go away.

This makes it impossible to reason about things, as sometimes I get different result using same exact code.

Is there something one can do to remove this internal error? Why it happens sometimes only?  Do I need to clear something before calling odetest to make sure same result is obtained each time?

interface(version);

`Standard Worksheet Interface, Maple 2024.2, Windows 10, October 29 2024 Build ID 1872373`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1841 and is the same as the version installed in this computer, created 2025, January 3, 8:59 hours Pacific Time.`

libname;

"C:\Users\Owner\maple\toolbox\2024\Physics Updates\lib", "C:\Program Files\Maple 2024\lib"

restart;

sol:=y(x) = 1/2*x*(-1-(1+I*3^(1/2))*((I*2^(1/2)-1+I)*(I*2^(1/2)+1+I)^2)^(2/3)-2*((I*
2^(1/2)-1+I)*(I*2^(1/2)+1+I)^2)^(1/3)-I*((I*2^(1/2)+I)^2-1)*3^(1/2)+(I*2^(1/2)+
I)^2)/((I*2^(1/2)-1+I)*(I*2^(1/2)+1+I)^2)^(1/3)/(I*2^(1/2)+I);
ode:=x^3+3*x*y(x)^2+(y(x)^3+3*x^2*y(x))*diff(y(x),x) = 0

y(x) = (1/2)*x*(-1-(1+I*3^(1/2))*((I*2^(1/2)+(-1+I))*(I*2^(1/2)+1+I)^2)^(2/3)-2*((I*2^(1/2)+(-1+I))*(I*2^(1/2)+1+I)^2)^(1/3)-I*((I*2^(1/2)+I)^2-1)*3^(1/2)+(I*2^(1/2)+I)^2)/(((I*2^(1/2)+(-1+I))*(I*2^(1/2)+1+I)^2)^(1/3)*(I*2^(1/2)+I))

x^3+3*x*y(x)^2+(y(x)^3+3*x^2*y(x))*(diff(y(x), x)) = 0

odetest(sol,ode,y(x));

Error, (in trig/normal/sincosargs) too many levels of recursion

odetest(sol,ode);

Error, (in trig/normal/sincosargs) too many levels of recursion

infolevel[odetest]:=5;

5

odetest(sol,ode);

odetest: Performing an implicit solution test

odetest: Performing an explicit (try hard) solution test

odetest: Performing an implicit solution (II) test

odetest: Performing another explicit (try soft) solution test

0

odetest(sol,ode,y(x));

odetest: Performing an implicit solution test

odetest: Performing an explicit (try hard) solution test

odetest: Performing an implicit solution (II) test

odetest: Performing another explicit (try soft) solution test

0

infolevel[odetest]:=0;

0

odetest(sol,ode,y(x));

0

restart;

sol:=y(x) = 1/2*x*(-1-(1+I*3^(1/2))*((I*2^(1/2)-1+I)*(I*2^(1/2)+1+I)^2)^(2/3)-2*((I*
2^(1/2)-1+I)*(I*2^(1/2)+1+I)^2)^(1/3)-I*((I*2^(1/2)+I)^2-1)*3^(1/2)+(I*2^(1/2)+
I)^2)/((I*2^(1/2)-1+I)*(I*2^(1/2)+1+I)^2)^(1/3)/(I*2^(1/2)+I);
ode:=x^3+3*x*y(x)^2+(y(x)^3+3*x^2*y(x))*diff(y(x),x) = 0

y(x) = (1/2)*x*(-1-(1+I*3^(1/2))*((I*2^(1/2)+(-1+I))*(I*2^(1/2)+1+I)^2)^(2/3)-2*((I*2^(1/2)+(-1+I))*(I*2^(1/2)+1+I)^2)^(1/3)-I*((I*2^(1/2)+I)^2-1)*3^(1/2)+(I*2^(1/2)+I)^2)/(((I*2^(1/2)+(-1+I))*(I*2^(1/2)+1+I)^2)^(1/3)*(I*2^(1/2)+I))

x^3+3*x*y(x)^2+(y(x)^3+3*x^2*y(x))*(diff(y(x), x)) = 0

odetest(sol,ode,y(x));

Error, (in trig/normal/sincosargs) too many levels of recursion

odetest(sol,ode,y(x));

Error, (in trig/normal/sincosargs) too many levels of recursion

odetest(sol,ode,y(x));

0

 

 

Download why_odetest_sometimes_fail_internal.mw

Add tracelast; after an error gives long output with this at end

...
#(\`trig/normal\`,8): sincosargs := [\`trig/normal/sincosargs\`(a)];
 \`trig/normal/sincosargs\` called with arguments: ((-2472*2^(1/2)+3496)*3^(1/2)-4288*2^(1/2)+6064)*(10+7*2^(1/2))^(1/2)+(6008*6^(1/2)-8496*3^(1/2)+10408*2^(1/2)-14720)*cos((1/24)*Pi)
 #(\`trig/normal/sincosargs\`,2): return op(map(procname,{op(x)}))
 \`trig/normal/sincosargs\` called with arguments: ((-2472*2^(1/2)+3496)*3^(1/2)-4288*2^(1/2)+6064)*(10+7*2^(1/2))^(1/2)
 #(\`trig/normal/sincosargs\`,2): return op(map(procname,{op(x)}))
 \`trig/normal/sincosargs\` called with arguments: (-2472*2^(1/2)+3496)*3^(1/2)-4288*2^(1/2)+6064
 #(\`trig/normal/sincosargs\`,2): return op(map(procname,{op(x)}))
 \`trig/normal/sincosargs\` called with arguments: (-2472*2^(1/2)+3496)*3^(1/2)
 #(\`trig/normal/sincosargs\`,2): return op(map(procname,{op(x)}))
 \`trig/normal/sincosargs\` called with arguments: -2472*2^(1/2)+3496
 #(\`trig/normal/sincosargs\`,2): return op(map(procname,{op(x)}))
 \`trig/normal/sincosargs\` called with arguments: -2472*2^(1/2)
 #(\`trig/normal/sincosargs\`,2): return op(map(procname,{op(x)}))

Not only is it random error, it also can not be cought using try/catch. So the whole program now stop and there is no way around it. If it was at least possible to trap the error, then it will not be a big deal. But when not even possible to trap Maple errors, then what is one to do? 

Hello

Following on from my earlier question:

https://www.mapleprimes.com/questions/239620-Round-Robin-With-Double-Bye

a colleague has produced (admittedly hurriedly) a sports schedule over 14 weeks for a 8-team double bye, and a 10-team over 15 weeks. 
Looking at it, and counting the possible combinations, neither seem optimal...

The 8 team has equal byes, the 10 uneven.

Edit. Ideally no team would have 2 byes in a row. 

Is there a solution in maple over these weeks? given the min duration would be 13 weeks and the max 15 weeks?
In the previous solution by mmcdara the 8 bye schedule each team has played 6 times after week 8, but since the roster is truncated to 14 or 15, there will be some weeks when no byes are required (all teams playing) to even things up.
Similarly, the 10 bye each team has played 8 times after week 10, but since the roster is truncated to 14 or 15, there will be some weeks when no byes are required.

Any help would be welcome!
double_bye.xls

Edit: I made some counting errors. It's 28 and 45 as Carl pointed out
double_bye_revised.xls

Hey guys,

I have to solve a bunch of systems of polynomial equations und dome restrictions given by inequalitites. I have 8 variables, 8 equations and and 13 inequalitites. Since the simple solve or SemiAlgebraic command are not able to solve every system I tryd some other ways. Right now I try to bring the set of equations and ineqaulities in a better from or structure using RealTriangulize from the RegularChains library. Later on I want to take those results and use solve or SemiAlgebraic again, hoping, that Maple than finds the solutions and is not calculating for houres without a result. I already know, that you can have diffrent outputs for RealTriangularize (I know list, record, piecewise and zerodimensional, althought the last one is not really helpful). Since I want to go on wirking with the results I need to have them in a form, that I can read of the new equations and inequalities to put them into solve. Often that works totaly fine, but sometimes I get an output I dont understand. I understand what It means but I dont understand why Maple uses that type of output. If you have a look in the attached file you can see what I mean:

restart; with(RegularChains); eq_5334 := {y*(m*x-m-n+1)+(-x+1)*n-x = 0, (-p+t)*k+p*y-t = 0, (k-x-y)*t-k*p+y = 0, (-x-y+1)*t+(-k+y)*n+x*s = 0, (-x-y+1)*p+m*y^2+x-y = 0, (x^2-x)*m+y*(t-1)-n+1 = 0, -k*n+s*x = 0, m*x*y-p = 0, 0 < k, 0 < m, 0 < s, 0 < x, 0 < y, 0 < n+(t-1)*p, 0 < (m*y-1)*n+(1-p)*(m*x-m+1), 0 < (m*x-m-t+1)*p+m*y*(t-n), 1 < x+y, k < 1, m < 1, s < t, t < 1}; eq_5380 := {(-x-y+1)*p+m*x*y = 0, (-p+t)*k+p*y-t = 0, (k-x-y)*t-k*p+y = 0, (-x-y+1)*t+(-k+y)*n+x*s = 0, (m-1)*y^2+(-x+1)*y-p+x = 0, (x-1)*(m-1)*y-x^2-n+x = 0, m*x^2+(-m-n+1)*x+(-y+1)*n+t*y-1 = 0, -k*n+s*x = 0, 0 < k, 0 < m, 0 < s, 0 < x, 0 < y, 0 < n+(t-1)*p, 0 < (m*y-1)*n+(1-p)*(m*x-m+1), 0 < (m*x-m-t+1)*p+m*y*(t-n), 1 < x+y, k < 1, m < 1, s < t, t < 1}; eq_5382 := {(-x-y+1)*p+m*x*y = 0, y*(m*x-m-n+1)+(-x+1)*n-x = 0, (-p+t)*k+p*y-t = 0, (k-x-y)*t-k*p+y = 0, (-x-y+1)*t+(-k+y)*n+x*s = 0, (-x-y+1)*p+m*y^2+x-y = 0, m*x^2+(-m-n+1)*x+(-y+1)*n+t*y-1 = 0, -k*n+s*x = 0, 0 < k, 0 < m, 0 < s, 0 < x, 0 < y, 0 < n+(t-1)*p, 0 < (m*y-1)*n+(1-p)*(m*x-m+1), 0 < (m*x-m-t+1)*p+m*y*(t-n), 1 < x+y, k < 1, m < 1, s < t, t < 1}; sys := eq_5334; SuggestVariableOrder(sys); R := PolynomialRing(%); dec_5334 := RealTriangularize(sys, R, output = piecewise); sys := eq_5380; SuggestVariableOrder(sys); R := PolynomialRing(%); dec_5380 := RealTriangularize(sys, R, output = piecewise); sys := eq_5382; SuggestVariableOrder(sys); R := PolynomialRing(%); dec_5382 := RealTriangularize(sys, R, output = piecewise); sys := eq_5382; SuggestVariableOrder(sys); R := PolynomialRing(%); dec_5382_record := RealTriangularize(sys, R, output = record)

[AlgebraicGeometryTools, ChainTools, ConstructibleSetTools, Display, DisplayPolynomialRing, Equations, ExtendedRegularGcd, FastArithmeticTools, Inequations, Info, Initial, Intersect, Inverse, IsRegular, LazyRealTriangularize, MainDegree, MainVariable, MatrixCombine, MatrixTools, NormalForm, ParametricSystemTools, PolynomialRing, Rank, RealTriangularize, RegularGcd, RegularizeInitial, SamplePoints, SemiAlgebraicSetTools, Separant, SparsePseudoRemainder, SuggestVariableOrder, Tail, Triangularize]

 

[s, k, n, p, m, t, x, y]

 

R := polynomial_ring

 

dec_5334 := [[x*s+((-x^2+x)*m-t*y+y-1)*k = 0, (m*x*y-t)*k+(x+y)*t-y = 0, n+(-x^2+x)*m-t*y+y-1 = 0, -m*x*y+p = 0, (x^2*y+(y^2-y)*x-y^2)*m-x+y = 0, t*y^2-y^2+x = 0, (15*y^2+24*y+20)*x-6*y^2-13*y-10 = 0, y^3-y-2 = 0, 0 < k, 0 < m, 0 < s, 0 < x, 0 < y, 0 < 12891634966*y^2+19613071879*y+16947294542, 0 < 1256597*y^2+1911761*y+1651926, 0 < 6310892468*y^2+9601263717*y+8296275330, 0 < 1401*y^2+2130*y+1840, 0 < 1-k, 0 < 1-m, 0 < 72927541996846438*y^2+110950482461140595*y+95870270479707846, 0 < 1-t]]

 

[s, k, n, p, m, t, y, x]

 

R := polynomial_ring

 

dec_5380 := piecewise(`and`(`and`(`and`(0 < x^3-2*x^2+3*x-1, 0 < x^3+2*x^2+x-1), x^3+x^2+x < 1), 0 < 3*x-1), [[s*x+((1-x)*y*m+(x-1)*y+x^2-x)*k = 0, (m*y^2-y^2-t+(1-x)*y+x)*k+(y+x)*t-y = 0, n+(1-x)*y*m+(x-1)*y+x^2-x = 0, p-m*y^2+y^2+(x-1)*y-x = 0, m*y-x-y+1 = 0, t*y^2+(x-1)*y^2+(2*x^2-2*x)*y+x^3-2*x^2+x = 0, (3*x-1)*y^2+(3*x^2-3*x)*y+x^3-2*x^2+x = 0, 0 < k, 0 < m, 0 < s, 0 < y, 0 < -6*x^6-9*x^5*y+20*x^5+27*x^4*y-27*x^4-32*x^3*y+19*x^3+17*x^2*y-7*x^2-3*x*y+x, 0 < 3*x^6+3*x^5*y-14*x^5-10*x^4*y+26*x^4+11*x^3*y-24*x^3-3*x^2*y+11*x^2-2*x*y-2*x+y, 0 < 6*x^5+9*x^4*y-17*x^4-18*x^3*y+17*x^3+11*x^2*y-7*x^2-2*x*y+x, 0 < y+x-1, 0 < 1-k, 0 < -m+1, 0 < t-s, 0 < 1-t]], [])

 

[s, k, n, p, m, t, x, y]

 

R := polynomial_ring

 

dec_5382 := piecewise(`and`(`and`(y^3-2*y^2+y < 1, 0 < y-1), 23*y^3-37*y^2+13*y-3 <> 0), [[-k*n+s*x = 0, (p-t)*k+(y+x)*t-y = 0, (y+x-1)*n+(-x*y+y)*m+x-y = 0, (y+x-1)*p-m*y^2-x+y = 0, m*y-1 = 0, t*y^2+x^2+(y-1)*x-y^2 = 0, x^3+(3*y-2)*x^2+(2*y^2-3*y+1)*x-y^3+y^2 = 0, 0 < k, 0 < s, 0 < x, 0 < -2*x^2*y^2-2*x*y^3+2*y^4+x^2*y+3*x*y^2-3*y^3-x*y+y^2, 0 < x^2*y^2+2*x*y^3+y^4-x^2*y-4*x*y^2-3*y^3+2*x*y+3*y^2-y, 0 < -x^2*y-x*y^2+y^3+x*y-y^2, 0 < y+x-1, 0 < 1-k, 0 < t-s, 0 < 1-t]], 23*y^3-37*y^2+13*y-3 = 0, [[-k*n+s*x = 0, (p-t)*k+(y+x)*t-y = 0, (y+x-1)*n+(-x*y+y)*m+x-y = 0, (y+x-1)*p-m*y^2-x+y = 0, m*y-1 = 0, t*y^2+x^2+(y-1)*x-y^2 = 0, (2377326*y^2-1587000*y+302588)*x^2+(390793*y^2+497766*y+138115)*x-507805*y^2+152032*y-109047 = 0, 23*y^3-37*y^2+13*y-3 = 0, 0 < k, 0 < m, 0 < s, 0 < x, 0 < y, 0 < 700112222844255556263586865*x*y^2-260269572171898884295316974*x*y-93795749047261033657544191*y^2+73822886321394794237709987*x+34866975665513154551125606*y-9877974587657378842117575, 0 < -26166721441919*x*y^2+9412709182291*x*y+53422638514257*y^2-3387596446782*x-21180373503698*y+6484087812711, 0 < 21236600258115*x*y^2-8079468597142*x*y-3053799376681*y^2+2340822678357*x+1387037467490*y-370794765921, 0 < y+x-1, 0 < 1-k, 0 < -m+1, 0 < t-s, 0 < 1-t]], [])

 

[s, k, n, p, m, t, x, y]

 

R := polynomial_ring

 

`Non-fatal error while reading data from kernel.`

(1)

NULL

I would like to get results like in dec_5334. I can easily go on working with this kind of form. In dec_5380 you can see a diffrent output. I dont see the point of giving me this output. the second line i basically epmty. and in the first line the solution is broken into peaces. when a certain solution just works under some inequalitites, why dont they put those four inequalities inside of the list in front of it? Is there a workaround for the "normal" output? Or is there a way to read off the lines from this kind of structure, with the open { in front ?

The same problem appears in dec_5382. WHy dont give me a list with to lists of equations and inequalities to show me both solutions?
In the last example dec_5382_record you can see the output when you change the corresponding option in RealTrinagularize. But here I again have the problem that I dont know how to read of the equations and inequalities from the open curly bracket.

If anyone could help me, I would be very glad. Thank yu in advance.

Regards

Felix

Download Output_of_RegularChains.mw


Does any one have any idea to demonstrate, using Maple, that for any couple (a, b) of strictly positive integers

(a*b)! / (a! * (b!)^a) 

is an integer?

Hi

Can someone improve my AI code so I get to the final team's config directly, rather than a series of set iterations? thanks 

teams.mw

set 1: Michael K, Andy C
set 2: Michael G, Mitch
set 3: Jez, Dean B
set 4: Anthony B, Rik B
set 5: Ilya, Fariborz
set 6: Eugene, Tania
set 7: Bill, Stevs
set 8: Victor, Jane
set 9: Nash, Ben
 

Why doesnt this example work in my Maple 2021.1 from the user manual?

restart;
L := [seq(i, i = 2 .. 1000)];
divisor := 2;
while (numelems(L) > 0)  do  divisable,  L:=selectremove(i->(i mod divisor=0), L):
Error, unterminated loop

n:=numelems(divisable);  

if (n>0) then  printf("%d integers%s whose smallest prime divisor is %d\\n",n,  'if'(n>1, "s", ""), divisor):  end if;  

divisor :=nextprime(divisor);  

end do:
Error, unable to parse
 

Is there a way to put in intervals and get the output as inequality Notation? Something like this ->

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