Originally Posted by

**Prometheus** I got the problem of finding an approximation for the eigenvalue of

$\displaystyle y'' + \lambda (1+\varepsilon x) y = 0$

when $\displaystyle \varepsilon$ is small, and $\displaystyle 0<x<\pi$

I don't know a lot when it comes to ODE, so I have no idea how to approach this. I mean, I know the basics of ODE but never got to the sturm liouville systems. (It looks like a simple problem, but I never saw anything similar so I don't know what I should do here)

any help would be appreciated. also, if anyone know of any books\sites that have some other examples of this type, it would be great too.