A Method to Tackle First Order Differential Equations with Liouvillian Functions in the Solution

TL;DR

This paper introduces an extended algorithm based on the Prelle-Singer method to solve a broader class of first order differential equations involving Liouvillian functions, addressing limitations of previous approaches.

Contribution

An extended algorithm that successfully solves many previously unsolvable LFOODEs, enhancing the Prelle-Singer method's capabilities while maintaining its semi-decision nature.

Findings

Successfully solves a large class of LFOODEs

Extends the applicability of the Prelle-Singer method

Maintains the semi-decision characteristic of the original approach

Abstract

We present an algorithm to solve First Order Ordinary Differential Equations (FOODEs) extending the Prelle-Singer (PS) Method. The usual PS-approach miss many FOODEs presenting Liouvillian functions in the solution (LFOODEs). We point out why and propose an algorithm to solve a large class of these previously unsolved LFOODEs. Although our algorithm does not cover all the LFOODEs, it is an elegant extension mantaining the semi-decision nature of the usual PS-Method.