First off, I've never taken a differential equations class. This is for my Math Methods for Physicists class, and we are on the topic of DE. Unfortunately, we didn't cover this much, so most of what I am about to show you comes from the professor giving me tips and my own common sense. I'd really like to learn this stuff, but I have no idea what I am doing. 1. The problem statement, all variables and given/known data Find the basis functions that result from the differential equation u''(x)=-k^2u(x) and these boundary conditions: u(0)=u(L) u'(0)=u'(L) 2. Relevant equations 3. The attempt at a solution I don't know how to code in Latex yet, so forgive me for having to use a picture of my work thus far. Again, most of this is from other's help and common sense. I couldn't begin to explain what is going on here, or its uses. Since the image is too big to be displayed, here is the link to it on my imgur account: http://imgur.com/D8B3U Thanks!