Chapter 1.3, Problem 10P

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.

$\frac{d}{dx}\left[\left(1-x^2\right)\frac{d}{dx}{P}_n\right]+n(n+1)P_n=0,n$ constant