1. The problem statement, all variables and given/known data Find the eigenvalues and the eigenfunctions for x^2y"+2xy'+λy = 0 y(1) = 0, y(e^2) = 0 2. Relevant equations See problem 3. The attempt at a solution My book has one paragraph on this that does not help me. I tried using an auxiliary equation and solving for lambda. I get (m+√λ)^2 a real number with duplicity two. I don't know what to do with this or if this is even the right first step. The SINGLE paragraph on this doesn't explain anything (it's practically a side note) I would appreciate some guidance. There are two problems like this on the take home quiz and we didn't go over it in class so I am very lost and confused. Also I've been pounding my head over this with my directionless fury. Help subside my hate! Thanks for your time everyone!