An algorithm for computing exponential solutions of first order linear differential systems

Abstract

This article deals with the computation of exponential solutions of first order linear differential systems with rational function coefficients. We develop an algorithm working dlrectly at the system in contrast to the standard approach of cyclic vectors which transforms the system in an equivalent nt h order scalar linear differential equation. We have implemented our method in the computer algebra system MAPLE V, and it turns out that it is in general more efficient than the cyclic vector approach.