Boundary value problem for Laplace's equation (Dirichlet Problem)

Boundary value problem for Laplace's equation (Dirichlet Problem). See attached file for full problem description.

Sturm-liouville problems

1. find the eigenvalues and eigenfunctions of the boundary- value problem y''+λ y = 0 , y(0) = 0 , y(π /4) = 0 ( n = pie) 2. find the eigenvalues and eigenfunctions of the boundary- value problem y''+(λ+1) y = 0 , y'(0) = 0 , y'(1) = 0 3. find the sqaure norm of the following problem along with the eigenvalues and eigenfunctions y''+λy = 0 , y'(0) = 0 , y(1) + y'(1) = 0

pleas answer number 18 only

number 18. please dont do the CAS nor the plot

please answer only number 17

Book:- Differential Equations, by Dennis G Zill, page ,number 17 or se attachment below, thanks.

Sturm-liouville problem

1. (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. 2. 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.