I have the following BVP:
$(\alpha+x)y''+y'+\lambda^2 y=0$, with the following boundary condition:
$y(x=L)=0$ and $y'(x=0)+\lambda^2 y(0)=0$,
where $\alpha$ is some constant, $x$ is a parameter and $\lambda$ is an eigenvalue. I tried to solve it but the orthogonality condition is not satisfied for this case. I assume it has to do with the (2) B.C. Any suggestions?, What is the physical meaning of this?