1. ## approximation for eigenvalues

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.

2. 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.
I suggest doing a search on "perturbation theory" in google or in bing, there is much stuff out there.