I agree with Preben (in the above link), you will need numerical ways.

The first equation means to write y = r1*(q1-x)*(1+x)/q1 and after substituing that into the second equation one gets

(1+x)*r2*exp(-r1*(q1-x)*(1+x)/q1) = (1+x)*r2*q2-x

to be solved for x

I get solution close to zero, magnitude depending on N, something like 1e-28

no solution in any time, it seems ... the one you see may be a (numerical) artefact - except you can justify it. Have you feed it into your problem and studied the relativ and absolute errors?

PS: are you *sure* that you can use floats? Or: why do you not provide exact values? May be that is (one) reason ...

a) Using simple quotation remarks 'P' and "eval" or "value" should do (I would prefer "Sum" instead of "sum")

b) Consult Maple's help on recursive function for a proper usage, especially "option remember".

PS: Would be interested to see a solution for the inital recursion (if ever possible)

Hm ... I learned that fct(t) makes a substitution.

Though from Math I would always expect that t is a 'local' variable w.r.t. integration, without using a tricky workaround.

PS: I can not see, wether Int or int was used in the original question (but that's probably minor)

Dirac is not a function

1) one can not integrate numerically or has to "approximate" Dirac, sometimes it helps to use integration by parts to have Heaviside

2) formally the help pages tell how to "read" Int( Dirac(x) * f(x), x in a range)

I have seen this through Mathematica rechnet falsch . But actually: how often have 'we' have been faced with bugs in MMA, Maple (here or elsewhere) or other systems. I do not see the point which is worth a paper. And a simple numerical crosscheck would show it (for serious usage one would do that, see contributions at this board).

I sometimes use something like below to have the 'definition' at hand

PP:=(x,m) -> Sum( Sum(binomial(m,k+p),k=1..m-p)*x^p,p=0..m-1);
P:= (x,m) -> eval( PP(x,m), Sum = add);

                  P := (x, m) -> PP(x, m)|
                                         |Sum = add
P(z,3);
                              2
                             z  + 4 z + 7

................................

Do not use the 'dot'

note that Maple is case sensitive, so use lambda, not Lambda (except you want to different variables)

gamma is a system constant, try it using g instead

Also note that you have more equations than parameters, so it could be that your system has no solution (I think so after a quick try)

Best would be to upload your sheet (green arrow at the end of the menu for writing contributions here) or provide them directly.

For me that is not "clear", perhaps you provide an example (hopefully not the Riemann thing ...)

And I have doubts that some CAS actually "proves" something, perhaps you mean it in an informal sense.

I do not want to interrupt the lecture by acer, but simply would write
f := g and fp := D(f) in that case.

f(1);
                                 g(1)

fp(1);
convert(%, diff);
                               D(g)(1)


                          / d       \|
                          |--- g(t1)||
                          \dt1      /|t1 = 1

If xi is a solution, then -xi is one as well, let me write y = sqrt(xi)
and t = sqrt(Omega), 0 <= t (I assume you mean Omega to be real). Then
solve the polynomial, plot its Re and Im for each solution.

(1/1200*(xi^2-1)^2+1-Omega^2)*(-Omega^2+xi^2)-xi^2 = 0;
eval(%, [xi=sqrt(y), Omega=sqrt(t)]): 
G:=collect(%, y);    # polynom in y of degree=3, parameter=t

sols:=[solve(%, y)]:
solsReIm:=map('q -> (Re(q), Im(q))', %):

plot(solsReIm, t=0 .. 0.02, color=
  [black, yellow,    # this will be the purely real solution
   red, blue,        # the first, complex solution
   magenta, green]); # the 2nd solution, complex

it is embedding objects in powerpoint ... not a Maple thing per se ...

animation in pdf is not a Maple theme (may be: Flash?)

besides: I do not allow to execute programs for a reader, not even js