Some remarks on the solution of linearisable second-order ordinary differential equations via point transformations

Transformations of differential equations to other equivalent equations play a central role in many routines for solving intricate equations. A class of differential equations that are particularly amenable to solution techniques based on such transformations is the class of linearisable second-orde...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2020-05
Main Author: Winter Sinkala
Format: Article
Language:English
Subjects:
Differential equations
Lie groups
Mathematical analysis
Ordinary differential equations
Transformations (mathematics)
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Transformations of differential equations to other equivalent equations play a central role in many routines for solving intricate equations. A class of differential equations that are particularly amenable to solution techniques based on such transformations is the class of linearisable second-order ordinary differential equations (ODEs). There are various characterisations of such ODEs. We exploit a particular characterisation and the expanded Lie group method to construct a generic solution for all linearisable second-order ODEs. The general solution of any given equation from this class is then easily obtainable from the generic solution through a point transformation constructed using only two suitably chosen symmetries of the equation. We illustrate the approach with three examples.
ISSN:2331-8422