Chapter 1.3, Problem 12P

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.

$\frac{d}{dx}\left[p(x)\frac{dy}{dx}\right]-q(x)y+\lambda r(x)y=0,\lambda$ constant