Here is a paper written by me: http://www.voofie.com/content/84/solving-linear-non-homogeneous-ordinary-differential-equation-with-variable-coefficients-with-operat/" [Broken] 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: http://www.voofie.com/content/6/introduction-to-differential-equation-and-solving-linear-differential-equations-using-operator-metho/" [Broken] At last, you may wanna read other differential equations related questions, discussions, articles and links from this http://www.voofie.com/concept/Ordinary_differential_equation/" [Broken].