NOTE ON KOVACICS ALGORITHM

Algorithms exist to find Liouvillian solutions of second order homogen eous linear differential equations (Kovacic, 1986, Singer and Ulmer, 1 993b). In this paper, we show how, by carefully combining the techniqu es of those algorithms, one can find the Liouvillian solutions of an i rreducible second order linear differential equation by computing only rational solutions of some associated linear differential equations. The result is an easy-to-implement simplified version of the Kovacic a lgorithm, based as much as possible on the computation of rational sol utions of linear differential equations. (C) 1996 Academic Press Limit ed