Explaining Sturm-Liouville Problem?

I am having trouble figuring out how to solve sturm-liouville problems. An example of one type of these problems is find the eigen values and eigen vectors of y'' + λy=0 when y'(0)=0, y(1)+y'(1)=0. Another one would be y'' +y' +5λy=0 when y(0)+y'(0)=0 and y(1)+y'(1)=0. Now the way my teacher explained to solve these are you say y=e^(ax) and then sub this into your equation. Then solve for "a". The way the book explains how to do this is that λ=+or - a^2. Can anyone explain to me whats going on and then what to do after finding λ? thanks