I'm having problems doing this BVP eigenvalue problem, and would appreicate if someone can help me through the next step
By setting $y=u/x$, find all eigenvalues and eigenfunctions of the Sturm-Liouville problem:
for $x \in [\pi, 2\pi]$ with BV's of $y(\pi)=y(2\pi)=0$
So I managed the first step, doing $y=u/x$ I changed the ODE into:
So then i'm supposed to find the lambda eigenvalues, but i'm having issues.
The only examples i've ever seen involve $y''+\lambda y=0$ with BV's $y(0)=y(L)=0$ never with $y=u/x$ and $y(\pi)=y(2\pi)=0$
I understand that I need to try $\lambda > 0$, with general solution:
But I don't know where to go from there, do I just sub the BV's $\pi$ and $2\pi$ in? I'm really confused. Any help would be greatly appriecated thanks.