Chapter 1.3, Problem 11P

Show that Eq. (10) can be matched to each equation in Problems $7$ through $12$ by a suitable choice of $n$, coefficients $a_0,a_1,a_2,\mathrm{...},a_n$, and function $g$. In each case, state whether the

equation is homogeneous or nonhomogeneous.

$\frac{d^{4}y}{d{t}^4}+(\cos t)\frac{d^{2}y}{d{t}^2}+y=e^{-t}\sin t$