# Sturm-Liouville: Expansion in Eigenfunctions

Hello, I need a detailed solution of the attached problem.

Consider the eigenvalue problem

y" + lambda^2 * y = 0

With the boundary conditions:

y(0) = y'(1)=0

1. Determine the eigenfunctions and eigenvalues.

2. show that the eigenfunctions are orthogonal.

3. Show how to expand a smooth function in terms of the eigenfunctions.

https://brainmass.com/math/numerical-analysis/sturm-liouville-expansion-eigenfunctions-229145

#### Solution Preview

Hello and thank you for posting your question to Brainmass!

The solution is attached below in two files. the files are identical in content, only differ in format. The first is in MS Word format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.

The equation

Is the simple harmonic equation.

Its solutions are:

And the ...

#### Solution Summary

The six page document gives a step by step solution to the harmonic equation and shows how to expand any function using the eigen functions.