Problem: find the eigenvectors and eigenfunctions of the following Sturm-Liouville problem:

What I did: since I can multiply by and rewrite as:

I substitute and find , so the general solution would be:

The condition gives . The second condition gives:

So i get and here I am stuck, because the Sturm Liouville eigenvalues are supposed to be real.... any suggestions on where I am wrong??

Thank you