Here is a paper written by me: Solving linear non-homogeneous ordinary differential equation with variable coefficients with operator method Basically, it uses operator method to solve linear non-homogeneous ordinary differential equation with variable coefficients. If you have a differential operator of order n, and you know a fundamental solution to the operator, you can use my method to factorize a linear factor out of the differential operator. By repeating the process, you can factorize the operator totally, and solving the equation is a matter of repeated integration only. (It doesn't teach you how to find a fundamental solution though. It is done probably by guessing.) I am not sure if this method is original. I just think of it a few days ago. People may have used it for a long time. But I can't find anything similar from the web. If you don't know what is operator method, please read this tutorial: Introduction to differential equation, and solving linear differential equations using operator method At last, you may wanna read other differential equations related questions, discussions, articles and links from this page in Voofie.