Or even for the general case sturm liouville system, how do you go about getting the eigenvalues and eigenfunctions? I really do not understand the lecture notes on this topic :P
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.