Have you tried using Laplace or Fourier transforms to solve this DE (since it is linear)?
The problem I am trying to solve is the following: I am to find the steady periodic solution of the differential equation.
F(t)= x''+2x where F is the even function of period 2pi such that F = sin(t) if 0<t<pi. I assume xp has the form AnCos(nt)+BnSin(nt), B =0 here
I did a fourier series expansion for sin (t) and got 2/pi +((2/pi) * summation from n=1 (n even) to infinity of (2/(1-N2)). I now went on to equate coefficients to find a xp with a known value of A, but got the incorrect answer. Is my procedure so far correct?