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exact solution of equation...

Asked by: Zeineb 530
integral-equation
August 25 2024
0  5

Dear all
I have an equation, I would like to dermine the exact solution, but maple return an error 

exact_solution.mw

Thank you

Update not downloading...

Asked by: C_R 2597
update windows10 installation
August 25 2024
0  4

On a Windows 10 installation with

I get after system restart and Maple launch

followed by

What could be the cause that the update is not downloading and how to fix it?

Error, (in evala) reducible RootOf detected. and s...

Asked by: nm 9934
solve ode differential-equations
August 24 2024
0  0

Maple solves this first order ode correctly and solution verifies OK. The solution is explicit and has RootOf. I asked it to solve it using dAlembert method to compare with my own solution using dAlembert.

Next I called dsolve on same ode and IC but asked for implicit solution now instead, then called solve on the implicit solution to see if it will give same solution y(x) as before (with RootOf). But instead solve gives this internal error 

               Error, (in evala) reducible RootOf detected.  

Next called PDEtools:-Solve to see if it will give same error. It did not give error. But it also could not solve for y(x) either.

Any one has any idea why this error is generated by solve? Is this expected or not?

I was expecting same result as first call to dsolve which returned explicit solution. And why is PDEtools:-Solve do not generate same error? It must have run through different code path.

May be some one have some insight on this.

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.1, Windows 10, June 25 2024 Build ID 1835466`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1792 and is the same as the version installed in this computer, created 2024, August 22, 12:6 hours Pacific Time.`

> 

libname;

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

> 

ode:=(2*x+y(x))+(4*x-2*y(x)+1)*diff(y(x),x)=0;
IC:=y(1/2)=0;

2*x+y(x)+(4*x-2*y(x)+1)*(diff(y(x), x)) = 0

y(1/2) = 0

> 

maple_sol:=dsolve([ode,IC],[dAlembert]);

y(x) = RootOf((8*I)*exp((3/41)*41^(1/2)*arctanh((1/41)*(-28*x+6*_Z-5)*41^(1/2)/(-4*x+2*_Z-1)))*9^(1/2)*x+48*(-(16*_Z^2-40*_Z*x-16*x^2-13*_Z+6*x+2)/(-4*x+2*_Z-1)^2)^(1/2)*_Z*x*exp((3/41)*41^(1/2)*arctanh((19/123)*41^(1/2)))-96*x^2*(-(16*_Z^2-40*_Z*x-16*x^2-13*_Z+6*x+2)/(-4*x+2*_Z-1)^2)^(1/2)*exp((3/41)*41^(1/2)*arctanh((19/123)*41^(1/2)))+I*exp((3/41)*41^(1/2)*arctanh((1/41)*(-28*x+6*_Z-5)*41^(1/2)/(-4*x+2*_Z-1)))*9^(1/2)+6*(-(16*_Z^2-40*_Z*x-16*x^2-13*_Z+6*x+2)/(-4*x+2*_Z-1)^2)^(1/2)*_Z*exp((3/41)*41^(1/2)*arctanh((19/123)*41^(1/2)))-36*x*(-(16*_Z^2-40*_Z*x-16*x^2-13*_Z+6*x+2)/(-4*x+2*_Z-1)^2)^(1/2)*exp((3/41)*41^(1/2)*arctanh((19/123)*41^(1/2)))-3*(-(16*_Z^2-40*_Z*x-16*x^2-13*_Z+6*x+2)/(-4*x+2*_Z-1)^2)^(1/2)*exp((3/41)*41^(1/2)*arctanh((19/123)*41^(1/2))))

> 

odetest(maple_sol,[ode,IC])

[0, 0]

> 

maple_sol:=dsolve([ode,IC],[dAlembert],implicit);

-((1/64)*I)*(64*x+8)*exp((3/41)*41^(1/2)*arctanh((1/41)*(28*x-6*y(x)+5)*41^(1/2)/(4*x-2*y(x)+1)))*exp(-(3/41)*41^(1/2)*arctanh((19/123)*41^(1/2)))/(((16*x^2+40*x*y(x)-16*y(x)^2-6*x+13*y(x)-2)/(4*x-2*y(x)+1)^2)^(1/2)*(4*x-2*y(x)+1))+x+(1/8)*(4*((16*x^2+40*x*y(x)-16*y(x)^2-6*x+13*y(x)-2)/(4*x-2*y(x)+1)^2)^(1/2)*exp(-(3/41)*41^(1/2)*arctanh((1/41)*(28*x-6*y(x)+5)*41^(1/2)/(4*x-2*y(x)+1)))*x-2*((16*x^2+40*x*y(x)-16*y(x)^2-6*x+13*y(x)-2)/(4*x-2*y(x)+1)^2)^(1/2)*exp(-(3/41)*41^(1/2)*arctanh((1/41)*(28*x-6*y(x)+5)*41^(1/2)/(4*x-2*y(x)+1)))*y(x)+((16*x^2+40*x*y(x)-16*y(x)^2-6*x+13*y(x)-2)/(4*x-2*y(x)+1)^2)^(1/2)*exp(-(3/41)*41^(1/2)*arctanh((1/41)*(28*x-6*y(x)+5)*41^(1/2)/(4*x-2*y(x)+1))))*exp((3/41)*41^(1/2)*arctanh((1/41)*(28*x-6*y(x)+5)*41^(1/2)/(4*x-2*y(x)+1)))/(((16*x^2+40*x*y(x)-16*y(x)^2-6*x+13*y(x)-2)/(4*x-2*y(x)+1)^2)^(1/2)*(4*x-2*y(x)+1)) = 0

> 

#solve gives error
sol:=solve(maple_sol,y(x));

Error, (in evala) reducible RootOf detected.  Substitutions are {RootOf(6*RootOf(_Z^2-41,index = 1)*_Z+41*_Z^2+5,label = exptmp) = -5/41*RootOf(_Z^2-41,index = 1), RootOf(6*RootOf(_Z^2-41,index = 1)*_Z+41*_Z^2+5,label = exptmp) = -1/41*RootOf(_Z^2-41,index = 1)}

> 

#PDEtools:-Solve  gives no error but does not solve it
sol:=PDEtools:-Solve(maple_sol,y(x));

> 

 


 

Download reducible_rootof_detected_august_24_2024.mw

Empty context panel: when does this happen ...

Asked by: C_R 2597
context-menu duplicate-question
August 24 2024
1  1

I am trying to understand under which conditions submenus disappear.

Now I have seen that the context panel is empty when submenues disappear.

Has anybody noticed the same and are there other instances when the context panel is emtpy?

Both effects could have the same rootcause.

Here is an example:
A -> no submenu

B -> Empty context panel

C -> Menu appears inside workspace (first time I see that)