Find the eigenvalues and corresponding eigenfunctions of the given BVP.

Answer:

So, through substitution, I found that the given equation transforms to the simple harmonic equation:

where

y=At+B when lambda=0

when lambda<0 *sorry, can't get the latex to work for me: it's meant to be to the power of e

lambda>0

I then put the equation in the form of a sturm liouville system by multiplying by factor such that I got:

However, I was then unsure of how to go about getting the required eigenvalues and eigenfunctions due to the y(a)=0 boundary condition. Thanks in advance.