An extension of the Prelle–Singer method and a Maple implementation

Abstract

The Prelle–Singer method is a semi-decision algorithm which can be used to solve analytically first order ordinary differential equations which have solutions in terms of elementary functions. In this paper we develop an extension to the Prelle–Singer method which deals with first order ordinary differential equations whose solutions lie outside the scope of the standard Prelle–Singer method. We present a software package in Maple V, Release 5 which implements both the Prelle–Singer method in its original form and our extension. Tests with ordinary differential equations taken from standard references show that our package is able to solve equations where Maple's standard solution routines fail.