@C_R 
Some answers :-) 
1) Did not check it , so ? 
2) Must be possible , a procedure is a general approach.
Because the module code can answering different experiments , it must be  general coded, otherwise you can do only one experiment if it is not general coded.
Every new experiment code example must be hardcoded with new data.if you don't use procedures.
3) Possible, but needs more time, there is the known start example and all other examples  are variants with different boundaries
4) ChatGpt paid plus ( cheaper one possible , i think ) now with  GPT plugin : mathematical statistics ( makes those posters) 
5) BC4  is there for the mathematival completeness, but has no influence i think on the calculation

It’s important to be able to define the boundary regions.
This module code can be expanded even further to heat or cool the rod in different ways (that’s also possible)
I put this module code together quickly, so there may well be some errors in it.

I've encountered nonlinear PDEs before that require different solution techniques, but I also find this linear PDE for heat to be complicated

Rod with different boundries conditions
staaf_module_met_wisselnde_boundriesDEFvoorlopig_18-7-2026.mw

corrected rod boundry conditions 

Download pde_heat_1D_oplossing_van_mprimes_misschien_correctie_17-7-2026.mw

boundry conditions for this rod setup 

@Rouben Rostamian  
Thanks for pointing this out
I'm not entirely sure what you mean exactly, but got a idea of it 
Yes, i am interested in the details of this setup 

https://www.dropbox.com/scl/fi/cuexecaf3x4wd5vwi28gv/pde-warmet-cilindrische-staaf.png?rlkey=9gob68msfpsdbksuemcxtwtiz&st=t6d7q09s&dl=0

restart:

infolevel[pdsolve] := 3:

assume(k > 0, L > 0):

PDE1D :=
    diff(V(z,t),t)
    =
    k*diff(V(z,t),z$2):

BC1 :=
    -k*D[1](V)(0,t)
    =
    q(t):

BC2 :=
    D[1](V)(L,t)
    =
    0:

IC :=
    V(z,0)
    =
    0:

problem1D := {PDE1D, BC1, BC2, IC}:

sol1D := pdsolve(
    problem1D,
    V(z,t)

This seems the right conditions for this experiment?

BC1 := -k*D[2](T)(r,0,t) = q(t);
BC2 := D[2](T)(r,L,t) = 0;
BC3 := D[1](T)(R,z,t) = 0;
BC4 := D[1](T)(0,z,t) = 0;
IC  := T(r,z,0) = 0;

@Earl 
Hello Earl , the display command ends with : (surpressing outcome),  use  ;  

3_regions_-_proceedure_-velocity_-temperatuur_profielen_7-7-2026.mw
a array plot ...?

Most close to get , so there is more involved ?
most_close_table_to_get_mprimes_7-7-2026.mw
Module code ( start)
3_regions_mprimes-verbeteringen_8-7-2026.mw

 

@dharr 
Thanks, Ctrl J, K  and Ctrl T gives text  and Ctrl M / Ctrl R  seems to me the important key combinations for working in Maple. 
Ctrl .  gives a section , handy too.
Ctrl  Z and Ctrl  X , do and undo. 

Does it depend on the solution family of the ODE that Maple apparently chooses?

Your expectation that the ODE output always uses set notation is probably not always possible.

@acer 

"Just to be clear, that P formula represents a product of terms (and not a sequence)."?

Just to be clear, that P formula represents a product of factors (and not a sequence)

Terms are used in a sum. 
Something went wrong with the message I wrote earlier, and a sentence was left out.
So it is a correction on your earlier sentence.

@acer 
"Just to be clear, that P formula represents a product of terms (and not a sequence)."?

Terms are related to a sum.

@Alfred_F 
Earlier versions of  Maple :  Maple's start-up message, 'Command the brilliance of 1,000 mathematicians'. :-)
 

Thus, from a mathematician’s perspective, this framework is essentially a symbolic ansatz engine expressed in neural-network notation. This also explains why the method ultimately yields explicit analytical formulas, such as Equation (12), rather than a trained predictive model.

In other words, the neural-network architecture serves primarily as a structured language for generating candidate solution families, while the actual determination of the parameters is carried out analytically through algebraic constraints derived from the differential equation. The process therefore resembles symbolic computation and exact-solution techniques far more than modern machine-learning approaches based on optimization and training.