Thanks for both answers! I had no problems understanding the analytical method Preben submitted. I didnt get exactly what was done in the numerical approach (I am not into the Proc stuff yet) but i dont want to bother you with teaching a newbie :D

@PatrickT:

I understood the first three paragraphs of your answer although i dont know how to convert the boundary conditions into equivalent initial conditions (meaning that the IC will provide a function which will satisfy the BC).

I tried out your recipe which worked:

 eq1 := diff(y(x), x) = a/sqrt(-a^2+x^2);
 eq2 := subs(a = 1, eq1);#I think doing this leads to only be able to fulfill just one BC unless you choose the right a!
 ics := y(5) = 1;
 soln1 := dsolve({eq2, ics}, 'type' = numeric);
 soln1(5);

However i cannot satisfy the second BC (y(5)=10).

So i tried the same with the two conditions and without providing a value for a

 ics := y(5) = 1, y(10) = 5;
 eq3 := diff(y(x), x) = a/sqrt(-a^2+x^2);
 soln2 := dsolve({eq3, ics}, 'type' = numeric, parameters = [a]);

This gives the following error:

Error, (in dsolve/numeric) cannot numerically solve a parametric boundary value problem

What went wrong?

I added a maple file for convenience.

DifferentialEquation.mw