In this video (from 27.00 - 50.00, which you don't need to watch!) a guy shows how you can solve the general second order ode [itex]y'' + P(x)y = 0[/itex] using perturbation theory. However he points out that the domain must be finite in order for this to work, I'm wondering how you would phrase a question like this or how you would know when you are working with an infinite domain etc...? If I was just given [itex]y'' + x^2y = 0[/itex] & asked to solve it using perturbation theory I wouldn't know if I was getting into trouble about finite or infinite domains, how do I re-phrase the question so that it makes sense? Are there any other things that cross your mind that one should be careful about? Thanks for your time.