It is an eigenvalue problem in the general Sturm-Liouville setting.
Solve the characteristic polynomial for the various parameter values and compute the corresponding solutions.
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.