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odetest does not validate correct soluti...

nm 11443 Maple 2024
ode dsolve differential-equations
April 18 2024
1 0

I think I found another clitch in odetest.

dsolve gives correct solution to this first order ode with IC. But odetest does not verify that the solution is satisfied for the IC part, but only for the ode itself. 

Below worksheet confirms the solution is also valid for the IC.   So why odetest does not give 0 for the IC part?

``

> 

restart;

19644

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1727. The version installed in this computer is 1725 created 2024, April 15, 17:29 hours Pacific Time, found in the directory C:\Users\Owner\maple\toolbox\2024\Physics Updates\lib\`

> 

libname;

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

> 

ode:=x^2*diff(y(x),x)*cos(y(x))+1=0;
ic:=y(infinity)=Pi/3; #16/3*Pi;
sol:=dsolve([ode,ic]);
odetest(sol,[ode,ic])

x^2*(diff(y(x), x))*cos(y(x))+1 = 0

y(infinity) = (1/3)*Pi

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

[0, (1/3)*Pi]

> 

#we see that odetest think the solution does not verify the IC. But it does
> 

IC_eq:=Pi/3=limit(rhs(sol),x=infinity)

(1/3)*Pi = (1/3)*Pi

Download odetest_does_not_verfiy_correct_solution_maple_2024_april_18_2024.mw

I think what odetest did is not use limit when plugging in the values. That is why.

If we do not use limit, this is what happens:

IC_eq:=Pi/3=eval(rhs(sol),x=infinity)

And this explains the odetest output. It should have used limit.

ps. just in case also reported to Maplesoft support.

How to make ODESteps use the new nicer l...

nm 11443 Maple 2024
ode dsolve differential-equations
April 16 2024
1 0

I noticed that Student:-ODEs:-ODESteps does not use the newer subscripted constant of integrations for solution of odes which looks much nicer.

Is there a way to make it use same constant of integrations as dsolve() does? Compare  

This is on a worksheet using typesetting level extended. Worksheet is attached


 

> 

restart

18836

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1724 and is the same as the version installed in this computer, created 2024, April 15, 17:29 hours Pacific Time.`

> 

#to make Maple use the new constant of integrations. Is this still needed in Maple 2024?
dsolve(diff(y(x),x$9)=1,arbitraryconstants=subscripted):
pdsolve(diff(psi(x,t),x$9)=0,arbitraryfunctions=subscripted):
> 

ode := diff(y(x), x$2) + 2*y(x) = 0;
Student:-ODEs:-ODESteps(ode,y(x));

ode := diff(y(x), x, x)+2*y(x) = 0

"[[,,"Let's solve"],[,,((ⅆ)^2)/(ⅆx^2) y(x)+2 y(x)=0],["•",,"Highest derivative means the order of the ODE is" 2],[,,((ⅆ)^2)/(ⅆx^2) y(x)],["•",,"Characteristic polynomial of ODE"],[,,r^2+2=0],["•",,"Use quadratic formula to solve for" r],[,,r=(0+/-([]))/2],["•",,"Roots of the characteristic polynomial"],[,,r=(-ⅈ sqrt(2),ⅈ sqrt(2))],["•",,"1st solution of the ODE"],[,,y[1](x)=cos(sqrt(2) x)],["•",,"2nd solution of the ODE"],[,,y[2](x)=sin(sqrt(2) x)],["•",,"General solution of the ODE"],[,,y(x)=C1 y[1](x)+C2 y[2](x)],["•",,"Substitute in solutions"],[,,y(x)=C1 cos(sqrt(2) x)+C2 sin(sqrt(2) x)]]"

> 

#compare to this output
dsolve(ode,y(x));

y(x) = c__1*sin(2^(1/2)*x)+c__2*cos(2^(1/2)*x)


 

Download make_step_solution_use_new_constant_of_integration.mw

 

why mapleprimes removes tags from post?...

nm 11443 MaplePrimes
tags
April 14 2024
0 3

I noticed tags on the post  

https://mapleprimes.com/questions/238161-Why-Maple-Gives-Solution-To-Euler-Ode

keep disappearing. 

I added tags "differential equation" and "dsolve" and so on.  

Later on when I visit this site again I found the tags are all gone.

Why does Mapleprimes remove the tags on post?

Or is someone else removing the tags? If so, why? is something wrong with the tags I've added?

This happend twice on this one post. I noticed earlier today the tags were gone, so I added them again. And now I see the same thing. They are all gone.

Error, (in Typesetting:-Parse) too many ...

nm 11443 Maple 2024
typesetting latex odesteps
April 13 2024
1 1

I found that sometimes Maple gives

               Error, (in Typesetting:-Parse) too many levels of recursion

When using the Latex command on the output of Student:-ODEs:-ODESteps

Below is worksheet showing it works for some and gives error for others. Is there a workaround for this? I'd like to convert the steps to Latex.

This happens in worksheet using either Display->Typesetting level as EXTENDED or STANDARD

> 

restart;
> 

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1722 and is the same as the version installed in this computer, created 2024, April 12, 17:58 hours Pacific Time.`

> 

ode:=diff(y(x),x)=0;
the_output:=Student:-ODEs:-ODESteps(ode,y(x)):
latex(the_output)

diff(y(x), x) = 0

\begin{array}{ccc}
 & {} & \textrm{Let's solve}
\\
 {} & {} & \frac{d}{d x}y \! \left(x \right)=0
\\
 \textrm{•} & {} & \textrm{Highest derivative means the order of the ODE is}1
\\
 {} & {} & \frac{d}{d x}y \! \left(x \right)
\\
 \textrm{•} & {} & \textrm{Integrate both sides with respect to}x  
\\
 {} & {} & \int \left(\frac{d}{d x}y \! \left(x \right)\right)d x =\int 0d x +\mathit{C1}  
\\
 \textrm{•} & {} & \textrm{Evaluate integral}
\\
 {} & {} & y \! \left(x \right)=\mathit{C1}  
\\
 \textrm{•} & {} & \textrm{Solve for}y \! \left(x \right)
\\
 {} & {} & y \! \left(x \right)=\mathit{C1}  
\end{array}

> 

ode := diff(y(x), x, x, x ) + 3*diff(y(x), x, x) + 4*diff(y(x), x) + 2*y(x) = 0;
the_output:=Student:-ODEs:-ODESteps(ode,y(x)):
latex(the_output)

diff(diff(diff(y(x), x), x), x)+3*(diff(diff(y(x), x), x))+4*(diff(y(x), x))+2*y(x) = 0

Error, (in Typesetting:-Parse) too many levels of recursion

 

 

Download latex_error_ODE_steps_maple_2024_april_13_2024.mw

update: Reported to Maplesoft support.

Why Maple gives solution to Euler ode wh...

nm 11443 Maple 2024
ode dsolve differential-equations
April 12 2024
1 4

This second order (Euler type) ode has no solution for the given two initial conditions. but Maple gives solution with one unresolved constant of integration.

ode:=x^2*diff(y(x),x$2)-2*y(x)=0;
ic:=y(0)=4,D(y)(0)=-1;

sol_no_IC:=dsolve(ode)

The IC's are given at x=0 as a trick to see what Maple will do. We see that at x=0 there is division by zero. So no solution exist for these IC's. But see what happens

sol_with_IC:=dsolve([ode,ic])

It seems Maple simply threw away the part of the solution it could not handle due to the x=0 and just returned the rest.

odetest(sol_with_IC,[ode,ic])

The correct answer should have been the NULL solution (i.e. no solution). 

What Am I missing here? Why does Maple do this? Should Maple have returned such a solution?

Maple 2024 on windows 10.

update:

Reported to Maplesoft support.

update:

Here is another example ode. This is first order ode. Maple gives a solution that does not satisfy the initial condition also. I wish I can understand how Maple comes up with these solutions since when I solve these by hand I see it is not possible to satisfy the IC, hence no solution exist.

14876

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1722 and is the same as the version installed in this computer, created 2024, April 12, 17:58 hours Pacific Time.`

> 

restart;

14876

> 

ode:=diff(y(x),x)+y(x)/x=x^2;
ic:=y(0)=a;

diff(y(x), x)+y(x)/x = x^2

y(0) = a

> 

dsolve(ode)

y(x) = ((1/4)*x^4+c__1)/x

> 

sol:=dsolve([ode,ic])

y(x) = (1/4)*x^3

> 

odetest(sol,[ode,ic])

[0, a]

> 

Student:-ODEs:-ODESteps([ode,ic])

Error, (in Student:-ODEs:-applyICO1) numeric exception: division by zero

 

 

Download another_strange_solution_ode_maple_2024.mw

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