Does anyone know of any good links (or even books though preferably not as there's a chance I won't be able to acquire them ) which go through worked examples of solving inhomogeneous versions of the Legendre, Laguerre and Hermite equations.
Math stack exchange is great when you have a specific question , but a textbook is better when you want to learn material for the first time so I'm only really looking for external links.
To give some context here is an example of the sort of question I want to know how to solve :
Given that
$$\int_{-\infty}^{\infty}e^{-(x-a)^2}H_n(x)dx=\sqrt{\pi}2^na^n$$
Where $H_n$ is the Hermite polynomial of order n, with eigenvalue−2n, normalised so that $\int^{\infty}_{\infty}H_m(x)H_n(x)e^{-x^2}dx=2^n\sqrt{\pi}n!\delta_{n,m}.$
Find a solution to the inhomogeneous equation
$$\tfrac{d^2y}{dx^2}-2x\tfrac{dy}{dx}+y=e^{2ax}$$
a a constant.
Note: The reason I ask is I'm studying for an exam thats in a few weeks