How can I use maple and separation of variables ,solve the wave equation u_tt=u_xx for a string of lengh 4 with u(x,0)=sin (Pi/2 x) e^-x . u_t(x,0)=0.u(0,t)=0 and u(4,t)=0.

What is the weak solution integral equation for 

d² u(x)/dx² -(1+x² ) u(x)-1=0

How can I use separation of variable to solve heat equation u_t=u_{xx on a rod of length pi/4 with u(0,t)=0, u(pi/4)=0 and u(x,0)=x(pi/4-x)} 

then solve heat equation by laplace transform

How can I solve x^2 on -Pi..Pi and to evaluate this at x= Pi to prove that Sum(1/n^2, n= 1..infinity) = Pi^2/6.