@Carl Love 

Thank you Carl.
 

@acer 

Thank you acer.
 

I was about to forget: browse the Posts menu, ypu will find several smart works by @Rouben Rostamia, in particuler this one 
212624-Solving-Multispan-Euler-Beams-With

@jat741 

nm did all the work, you'd better thank him.

best regards

@nm 

By the way, I discovered months ago a site containing a lot of Maple vs Mathematica comparisons about the resolution of ODEs and PDEs. Unfortunately I have lost it since.
I've understood you were the one who manages this site?
Could you please send me up its adress?

TIA

@nm 

The word nonhomogeneous in the title was misleading :-)

@nm 

Hi, 

For what I understand h(x,t) =0, so you can simplifiy your general solution accordingly.

About the wotksheet: the OP has tried to code the "by hand method" to solve the heat equation by setting T(x, t)=a(x)*b(t) in order to obtain a couple of ODEs (b'(t)=C_b*b(t) and a"(t)=C_a*a(t) for suitable constants C_b and C_a)

Best regards

@vv 

Thank you vv

@acer 

So it was a well known crash cause.
I'm happy to read that it is corrected (even if, in the example I posted, I believe that  is better to avoid doing this stupid thing of sorting a null vector)

Are these crashes recorded somewhere?

They are really borring when you meet one, specially if they occur during the execution of a Maplet-based application (debuggibg is impossible AFAK)

Thanks for your comment

@vv 

"... the maximum point found was outside the interval of integration"
You're right I'd missed this point.
Thanks for pointing it out



 

@acer 

Thank you acer. 
Being iused to end all my lines with a colon or a semicolon (even if it's not necessary), I regularly get trapped by putting an after proc(...)

@vv 

Great, I hadn't had the idea to represent f by a piecewise function, nor had I even thought that it would have give a general solution.

Thanks

PS: if you have, let's say 10 thousand points and "only" 10 "classes" (here the second element od any List[i]), it's better to display 10 plots where each correspond to a points in the same "class", than to display 10 thousands points.

Here is an example with 12 classes
 

restart:

with(ColorTools):
with(plots):
with(Statistics):

r := rand(0.0 .. 1.0):
N := 10000:
X := Vector(N, i->r()):
Y := Vector(N, i->r()):
Z := X +~ Y: # +~ Vector(N, i->r()):

# these 2 lines mimic what a simple colorscheme does
c := EvenSpread(Color("RGB", "Yellow"), 12):
c := op~(1, NearestNamedColor~(c0, palette="X11"));

C   := floor~(Z *~ 12) +~ 1:
eps := (max-min)(Z) * 1e-8:
mZ  := min(Z)-eps:
MZ  := max(Z)+eps:
C := floor~( (Z -~ mZ) /~ (MZ-mZ) *~ 12) +~ 1:


# this is extremely lengthy

CodeTools:-Usage(
  display( seq(plot([[X[n], Y[n]]], style=point, symbol=solidcircle, symbolsize=15, color=c[C[n]]), n=1..N) )
);

LC := Vector(12, i->NULL):
for n from 1 to N do
  LC[C[n]] := LC[C[n]] , n
end do:

# while this is very fast
CodeTools:-Usage(
       display(
         PLOT(
           seq(
             POINTS(
                < X[[LC[n]]] | Y[[LC[n]]]>, 
                COLOR(RGB, op(NameToRGB24(c[n])/~255))
             ),
             n=1..12
           )
         )
       )
     ):

);

memory used=10.19MiB, alloc change=0 bytes, cpu time=80.00ms, real time=117.00ms, gc time=0ns

@acer 

Thanks.

Regarding your last remark, I noticed that a lot of questions invoking Maplets remain unanswered. Probably because some think of them as an old-fashioned or exotic technology?
You may not think this is quite honest, but I thought that omitting the word "Maplets" would increase the probability of getting an answer.

@vv 

Thank you vv.
I'm completely ignorant of all this, so I'm going to look to to the Autolt Script Editor to see it can be of any help