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

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