5. Rather than give you the second order linear differential equation, below are provided the solutions to the characteristic equation and the forcing function.
Give the form of the solution to the particular part, but do NOT solve for the coefficients.
(a) $\lambda = -1, -2$, $F(t) = t^2 + 3t$
(b) $\lambda = -2 \pm i$, $F(t) = e^{-2t}$
(c) $\lambda = -2 \pm i$, $F(t) = t^2e^{-2t}$
(d) $\lambda = -2, -2$, $F(t) = te^{-2t}$
(e) $\lambda = -1 \pm 8i$, $F(t) = e^t \cos(3t)$
