I'm trying to solve this initial value problem for a wave equation with a cosine term. I've been solving other wave IVPs using d'Alembert's formula but I'm not sure how to deal with the extra term in this equation. All / any help is appreciated.
$$ u_{tt} - c^{2}u_{xx} = \cos (x) \\ u(x,0) = 0 \\ u_{t}(x,0) = 0 $$
Update 1: I've reduced the problem to the homogeneous problem with the initial ICs and the non-homogenous problem with ICs = 0. I know that the solution to the homogenous problem is 0 but I still need to find the solution to the non-homogenous problem.