# Eigenvalue solutions of differential equations with boundary conditions.

Consider the equation: y'' + k*y = 0 with BC: y(0) = 0 , y() = a 0

Answer the following:

1. What are the restrictions on k such that there is a nontrivial solution?

2. Find a solution using eigenfunction expansion on [0,]

3. Find a solution to the differential equation using any method

4. Compare answers 2 and 3 show they are equivalent

Please see the attached file for the fully formatted problems.

keywords: eigenvalues, eigenfunctions, ODEs

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#### Solution Summary

Eigenvalue solutions of differential equations with boundary conditions are investigated. The solution is detailed and well presented.

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