Since you have a linear ODE with a right-hand-side composed of harmonic terms you know that you can solve for the homogenous and particular solutions at each frequency separately, so do just that and add them up?
Or simply take the real part of the complex exponential.
However, you have at least two terms C1*sin(t) and C2*cos(t) that will be resonant. That you have to make sure is properly handled (and meaningful).
HTH
