Computer Algebra Solving of Second Order ODEs Using Symmetry Methods

TL;DR

This paper presents an updated Maple package that uses Lie symmetry methods to analytically solve first and second order ordinary differential equations, streamlining the solving process and result verification.

Contribution

The paper introduces an enhanced ODEtools Maple package with new routines for solving, testing, and classifying 1st and 2nd order ODEs using symmetry methods.

Findings

Includes an ODE-solver based on Lie symmetry methods.

Provides commands for testing and classifying ODEs.

Enhances the usability of symmetry-based solving techniques.

Abstract

An update of the ODEtools Maple package, for the analytical solving of 1st and 2nd order ODEs using Lie group symmetry methods, is presented. The set of routines includes an ODE-solver and user-level commands realizing most of the relevant steps of the symmetry scheme. The package also includes commands for testing the returned results, and for classifying 1st and 2nd order ODEs.