Find a general solution of the ODE y + 2 y = r(t) with r(t) as

Find a general solution of the ODE y" + ω²y = r(t) with r(t) as given. Show the details of your work.

What kind of solution is excluded in Prob. 8 by |ω| ≠ 0, 2, 4, · · ·?

Data from Prob. 8

r (t) = π/4 |cos t| if -π < t < π and r(t + 2π) = r(t), |ω| ≠ 0, 2, 4, · · ·