Advice needed about strategy for solving 2nd Order differential equations

Hello everyone,

I was working today on finding the solution for a 2nd order linear homogenous variable coefficient equation. I used a change of the independent variable to simply the differential equation, but the search for an appropriate substitution took me quite a while. My question is, whats the best strategy for finding a change of variable? Are there any resources on the internet which list change of variables for various differential equations.

Thanks.