I was trying to find out why my solution was not validating for this ode. It turned out because I was using solve instead of PDEtools:-Solve. It took me sometime to find this.

This made huge difference on odetest to verify the solution.

This is very simple ode. We just need to integrate once. But first we have to solve for y'(x). 

And here comes the difference. When I used solve to solve for y'(x), odetest did not verify the solution.

When using PDEtools:-Solve, it did.

The difference is how each returned the solution for y'(x). Both have RootOf but written differently and this made the difference.

1) Why solutions are written differently? 

2) Is this to be expected? I have thought Solve uses same engine as solve below the cover.

3) is it possible to make solve give the same form as Solve or change to that form?

I am now changing more of my code to use PDEtools:-Solve because of this.

Download PDEtools_Solve_vs_solve_june_8_2024.mw

Update

Here is a counter example. Where now it is the other way around.

Using solve makes odetest happy, but when using PDEtools:-Solve odetest does not verify the solution.  Same exact ODE.   

Download PDEtools_Solve_vs_solve_june_9_2024.mw

So now I have no idea which to use. Sometimes solve works and sometimes Solve works. I  guess I have to now solve the ode both ways each time and see which works.

Should not  print("my matrix is ",A) at least print "my matrix is " even if A is not correctly filled/setup?

Notice that nothing shows on screen when using print (but lprint does)

Is this expected? If it makes any difference, I am using worksheet and this is my display options

Download why_print_empty_june_7_2024.mw

If I do    odetest(...,odeA) I get correct result. But if I do    odetest(...,odeB);  odetest(...,odeA);   now it gives wrong output for the odeA one. 

Same exact code. It just depends on the call done before it.

Why would issuing a command before changes the output of odetest? It seems Maple remembers something from last call. But I have no idea how to fix this.

Is there a way to tell odetest not to remember or cache any results from last calls? i.e. Can I clear its remember table before calling odetest??

This is messing all my testing now since I get different result each time depending on which call was made before. I can't do restart before testing each ode, since this is done in a loop.  I just need a way to tell Maple to clear its internal cache so that each call to odetest is not affected by last call result. 

Doing forget(odetest); before the call had no effect.

Reported to Maplesoft.

Worksheet below

Download why_different_result_from_odetest_june_6_2024.mw

Update

FYI, I got email from Maplesupport that Maple R&D group will look at this issue.

So hopefully this will be fixed in a future version of Maple.  

I am not able to find a workaround but doing tracing I see that odetest does rememebr something from last call but have no idea to fix this myself.

I can't figure this out. Same exact patmatch works in global worksheet. But fails inside a proc.

I am using same exact code. In proc, I am doing    a::anything where `a` is now local symbol ofcourse. In worksheet, it is global ofcourse. I make sure I clear `a` in worksheet each time also.

So why it pathmatch fail in the proc? I must be doing something wrong but do not see it.,
 

Here is screen shot in debugger showing patmatch failed inside the proc

Very strange. What do I need to change in the proc to make it work as in worksheet? 

Download patmatch_in_proc.mw

Is the following valid result from odetest? is returns 0^n when 0 was expected.

Is this a bug or valid result? Maple solution is correct, so I expected 0 only not 0^n as result.

Download strange_odetest_result_june_6_2024.mw

Update

Until this bug is fixed, I added the following to my code which checks for odetest result. it looks for 0^anything and changes it to 0. 

ode:=diff(y(x), x)^n= 0;
sol:=dsolve(ode);
stat:=odetest(sol,ode);
if patmatch(stat,0^a::anything) then 0; else stat; fi

gives    0

I found this problem when using odetest to check mysolution for this ode and was not getting 0 as expected,.

These two expressions are the same

e1:=-sqrt(-(exp(-2 + 2*x) - 2)*exp(-2 + 2*x))/(exp(-2 + 2*x) - 2);
e2:=1/sqrt(2*exp(-2*x)*exp(2) - 1);

Is there an automated way to simplify e1 to e2? Below are my attempts. The closest I got is 

simplify(e1) assuming real;

But that still does not give same as e2. I can do it by "hand" as shown. But I like to find automated way since this is done in code without looking at expression. So I can't use the "hand" method there.

We can assume everything in real domain.

Download simplification_june_6_2024.mw

How do I get the susset that contains unknowns on the rhs of the elements?

Download 2024-06-05_Q_Select_Remove_indet_elements.mw

We see that this ode (x + y(x))*(1+diff(y(x),x)) = 0  has 2 solutions, One when (x + y(x))=0 and one when (1+diff(y(x),x))=0. Maple gives 3 solutions. They are correct but why?

Also when changing (1+diff(y(x),x)) to (a+diff(y(x),x)) now it gives only two solution.

Why does this happen? Should it not just return 2 solutions in both cases? and more strange one

(x + y(x))^2 *(1+diff(y(x), x))=0; now it gives 4 solutions. But this is no different. We also have 2 solutions. One when (x + y(x))=0 and one when (1+diff(y(x), x))=0. This time the extra two solutions are complex. 

Download why_extra_solution_from_dsolve_june_5_2024.mw

Any idea why this sometimes happens? odeadvisor says ode is quadrature but when asking it to solve it using quadrature sometimes it works and sometimes not.

Am I doing something wrong?

Download sometimes_dsolve_works_on_quadrature_june_5_2024.mw

Any one could find why Maple 2024 gives Error, (in evalf/int) invalid arguments on this ode? Why is it even calling evalf in first place as this is all symbolic.

Also reported to Maplesof just in case.

Download odetest_internal_error_evalf_int_june_3_2024.mw

Probably I am missing the obvious. In the attached worksheet the for statement gives me all results as desired but if I try to put this in a procedure I only get the last value. Could someone help me out. Thank you  ProcQuestion.mw

I wanted to do 

map(X->odetest(X,ode) assuming x>0,[sol]) 

where sol are the solutions I wanted to test. The above does not work as is. After some trial and errors, I found this works

map(X->[odetest(X,ode) assuming x>0],[sol]) 

I am not sure why. But it works. Is this the above the correct way to add assuming to a command inside Map? Or is there a different way or better way to do this?

I want to stick to the map command as above and nothing else such as ~ or some other ones. I find map more clear to use for me.

Here is worksheet.

Download how_to_use_map_with_assuming.mw

These  are good example(s)  why I think Maple's simplify needs to be improved. 

Example 1

Given an expression which is zero for nonnegative x, one would expect simplify to simplify it to zero when told that x is positive. 

But nothing I tried with simplify worked. combine  figured it out.

But why? Is this not the job of simplify? 

The expression is 

e:=x-1/4*(-2+2*(4*x^2+1)^(1/2))^(1/2)*(2+2*(4*x^2+1)^(1/2))^(1/2);

Here is worksheet

Compare some other software on this same problem

It should be as simple as the above in Maple.

A user should not have to try 100 different commands in Maple to find which works.

simplify should have done it in first place. What Am I overlooking here?

Maple 2024

Download why_simplify_do_not_work_example.mw

EXAMPLE 2

In this example the expression is zero for x<0. Here nothing worked for me. This is challenge for Maple experts here to find the command to simplify this to zero. 

I know it is zero for x<0.

e := -1/2*(-2*x*sqrt(4*x^2 + 1) + (16*x^3*sinh(3/2*arcsinh(2*x)) - 8*x^2*cosh(3/2*arcsinh(2*x))*sqrt(4*x^2 + 1) + 4*sinh(3/2*arcsinh(2*x))*x - cosh(3/2*arcsinh(2*x))*sqrt(4*x^2 + 1))*sqrt(-2 + 2*sqrt(4*x^2 + 1)))/sqrt(4*x^2 + 1)

Using some other software gives

I'd like to find command to do the same in Maple. i.e. simplify it to zero. What else to try?

Download why_simplify_do_not_work_example_2.mw

I think I found another problem with odetest.  When solution is implicit, it fails to verify the solution against the ode when adding the IC. (not everytime, but in some cases).

But it does verify the solution against the ode when IC is not given. I give 3 examples.  Also at bottom is worksheet of all of this.

Example 1

restart;

ode:=diff(y(x), x) = sin(y(x));
ic:=y(0)=Pi/2;
mysol:=ln(tan(y(x)/2))=x;

It says solution satisfies the ode itself OK

odetest(mysol,ode);

gives 0

But adding IC now gives

odetest(mysol,[ode,ic]);

Which I am having hard time reading. Is it now saying the solution does not satisfy the ode or the IC? Both are supposed to be zero.

Are these not supposed to be in same order given? so it looks like if we go left to right, it is saying the solution do not satisfy the ode now but it does satisfy the IC. Right?

But before it said the solution satisfies the ode.

Also, we can see the IC is satisfied. Let do it by hand

eval(mysol,[y(x)=Pi/2,x=0])

              0 = 0

So why does it say solution satisfies the ode first, then when adding the IC, now it changed its mind?

Also, solving for y(x) from the implicit solution, now it verifies it OK  with the IC also:

ode:=diff(y(x), x) = sin(y(x));
ic:=y(0)=Pi/2;
mysol:=ln(tan(y(x)/2))=x;
mysol_explicit:=solve(mysol,y(x));
odetest(y(x)=mysol_explicit,[ode,ic])

          [0, 0]

You see. Same solution. But different result from odetest depending if it is implicit or explicit.

Is this supposed to happen or is this a bug in odetest I should report? odetest is supposed to handle both explicit and implicit solutions. I know my solutions are correct. I just use odetest for verification. I also plotted my solution against maple's solutions and they are exact match. 

Example 2

ode:=diff(y(x),x)=1+y(x)^2;
mysol:=arctan(y(x))=x;
ic:=y(0)=0;
odetest(mysol,ode);
odetest(mysol,[ode,ic]);

Gives 0 for the first call to odetest but gives [diff(y(x), x) - 1 - y(x)^2, 0] for the second call.

Changing the solution to explicit. now it verifies it

mysol_explicit:=solve(mysol,y(x));
odetest(y(x)=mysol_explicit,[ode,ic]);

Now it gives [0,0]

Example 3

ode:=diff(y(x), x) - 2*y(x) = 2*sqrt(y(x));
ic:=y(0)=1;
mysol:=ln(sqrt(y(x))+1)=x+ln(2);
odetest(mysol,ode);
odetest(mysol,[ode,ic]) assuming positive;

Gives 0 for the first call but  [diff(y(x), x) - 2*y(x) - 2*sqrt(y(x)), 0] but when using explicit it now verifies OK

mysol_explicit:=solve(mysol,y(x));
odetest(y(x)=mysol_explicit,[ode,ic]) assuming positive;

           [0, 0]

Maple 2024 on windows 10

Download odetest_implicit_problem_june_2_2024.mw

Simple question. I hope it has simple answer. I have always thought that what int() returns should match exactly what "default" result shows when using int() with the option _RETURNVERBOSE 

I mean exact match. But this below shows that int() result underwent some simplification as it is not the same as default.

restart;

integrand:=sin(x)/(sin(x) + 1);
maple_result_1 :=int(integrand,x);
maple_result_2 := int(integrand,x,'method'=':-_RETURNVERBOSE')[1]

Ofcourse maple_result_2 can be made the same as maple_result_1

simplify(rhs(maple_result_2)) assuming 0<x and x<Pi;

But this is beside the point. Why is "default" is not excatly the same as int() result?  It seems that int() does something more after obtaining the :"default" result as shown.

Should default not match exactly result from int() ?

Maple 2024.