Assignment:
Q1. (a) Find the eigenvalues and eigenfunctions of the boundary-value problem.
x2y'' + xy' + λ y = 0, y(1) = 0, y(5) = 0.
(b) Put the differential equation in self -adjoint form.
(c) Give an orthogonality relation.
Q2. Hermite's differential equation
y'' -2xy' + 2ny = , n = 0, 1, 2,...
has polynomial solutions Hn(x). Put the equation in self-adjoint and give an orthogonality relation.
Provide complete and step by step solution for the question and show calculations and use formulas.