Here is the problem:

y'' + 2y' + lambda*y = 0 y(0) + y'(0) = 0, y(1) = 0

I am supposed to show that all eigenvalues are real and then find all the eigenvalues and eigenfunctions.

I have never seen this kind of problem before and my prof did not cover this in lecture material. I know how to find eigenvalues and vectors for a given matrix but I'm not sure where to start for this one.

Thanks!