Hi, I'm trying to find the eigenfunctions and eigenvalues of

$\displaystyle x''(t)+2x'(t)+\lambda x(t) = 0$

with

$\displaystyle x(0) = x(1) = 0$.

First, should I write in self adjoint form? I found it is

$\displaystyle (e^{2t}x'(t))' + \lambda x(t) = 0$

But I don't know how to continue, all the previous examples ended in a harmonic oscillator type equation. Just a hint will be enough

Thanks.