In this communication, we present a method for computing the Liouvillian solution of second-order linear differential equations via algebraic invariant curves. The main idea is to integrate Kovacic's results on second-order linear differential equations with the Prelle–Singer method for computing first integrals of differential equations. Some examples on using this approach are provided. Copyright © 2010 IOP Publishing Ltd.
|Journal||Journal of Physics A: Mathematical and Theoretical|
|Publication status||Published - Oct 2010|
Invariant Algebraic Curves
Linear differential equation
Second order differential equation