In this example, i have a top module A. Inside it, I have module named my_RECORD (which happened to be option object) that I want to return back to caller when they call a proc.

Maple allows me to declare the proc to return my_RECORD. No problem., But when making a local variable inside the proc and using o::my_RECORD it complains  that my_RECORD does not exist. 

The solution is to change o::my_RECORD to o::A:-my_RECORD

My question why it did not complain the same way on the return value on the proc?   for me, they are both semantically the same. One says the proc returns this type, and the other says the local variable is this type. So why had to do A:-my_RECORD on one but not the other? 

Here is an example. Maple 2021.2 on windows 10.

Download A_no_lib.mw

I do not understand why  simplify(eq,size,assume =t::real); gives an error but simplify(eq,size) assuming t::real; does not.

Which is the correct way to use assumptions with simplify? Inside or outside? And why would it make a difference?

Maple 2020.2 on windows 10.

I know the above inert int looks strange, but this is why it is inert. Later on there will be change of variable to make the integration variable a single symbol again as in normal integration usage.

Download simplify_error.mw

Correction

Please ignore this question. dsolve does hang, but I had typo in the timelimit command itself when I wrote the test. Fixing this, now it timesout OK.

Maybe someone can look why dsolve hangs on this ode. But since timelimit does work, there is a workaround.

Original question

I was checking Maple's dsolve on this textbook problem

The book gives the answer in the back as

When using Maple's dsolve, I found it hangs. The stange thing, is that adding timelimit() also hangs. I can understand dsolve() hanging sometimes. But what I do not understand is why with timelimit it also hangs?

I've waited 20 minutes and then gave up. As you see, the timelimit is 20 seconds. May be if I wait 2 hrs or 20 hrs or 20 days, it will finally timeout. I do not know but can't wait that long.

Do others see same problem on this ode? Does it hang for you? How about on the mac or Linux?

During this time, I see mserver.exe running at very high CPU. I restarted Maple few times, but this did not help.

Maple 2021.2 on windows 10. May be one day Maplesoft will fix timelimit so it works as expected. 

Download test_ode_hang.mw

on DLMF page, they show this transformation on independent variable for second order ode

https://dlmf.nist.gov/1.13#Px7

About half way down the page, under Elimination of First Derivative by Change of Independent Variable section.

I tried to verify it using Maple dchange. But the problem it looks like dchange wants the old variable to be on the left side (z in this example) and the new variable (eta in this example) to be on the right side in the transformation. But on the above web page, it is the other way around.

Here are my attempts

restart;
ode:=diff(w(z),z$2)+f(z)*diff(w(z),z)+g(z)*w(z)=0;

tranformation:=eta=int(exp(-int(f(z),z)),z);

PDEtools:-dchange({tranformation},ode,known={z},unknown={eta});
PDEtools:-dchange({tranformation},ode,{eta},known={z});
PDEtools:-dchange({tranformation},ode,{eta});

All give errors

Error, (in dchange/info) missing a list with the new variables
Error, (in dchange/info) the new variables are not contained in the rhs of the direct transformation equations
Error, (in dchange/info) the new variables are not contained in the rhs of the direct transformation equations

The problem it does not seem possible to invert the transformation shown on the webpage, so that the old variable z show on the left side and the new variable (eta) on the right side.  

Why is this restriction on dchange  Since one tells it which is the new variable and which is the old variable? May be I am not using dchange correctly in this example.

Any suggestion for a workaround to use dchange to verify the above result?

Here is my hand derivation (pdf file attached also)

Can the above be done using dchange?

Maple 2021.2 on windows 10

sol.pdf

sometimes complicated equation is generated and attempt to solve it fail, which is OK. But there is a case, where Maple generates an internal error from solve(). The problem is that it is not possible to even capture this error using try...catch... end try so the whole program crashes.

Is there a way to trap such errors, so at least it can bypass it without solving it but without terminating the whole program? 

According to help it says

The try statement provides a mechanism for executing statements in a controlled environment, where errors will not just cause the execution to halt with no warning.

Well. The above is not really true.

Download dec_16_2021.mw