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

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