Derive equation (3.31) by guessing a solution of the form x ( t ) = A cos d t + B sin d

Derive equation (3.31) by guessing a solution of the form x(t) = A cos ω_dt+B sin ω_dt in equation (3.29).

2Fywd F(w w3) xp(t) = (3.31) cos wat + (w - w})?+ 472w}) (w - w?)+ 47?w} ) co* sinwat. F coswat (etwat + e-iwat). * + 2y +w?x (3.29) 2