Using Laplace transform to solve the IVP: y^{\prime \prime}+9 y=e^{-3 t}, \quad y(0)=0, \quad y^{\prime}(0)=0 we find the solution y(t)=\mathcal{L}^{-1}\left\{\frac{1}{(s-3)\left(s^{2}+9\right)}\right\}