Some remarks on the solution of linearisable second-order ordinary differential equations via point transformations
Abstract
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.
Cite
@article{arxiv.1904.02777,
title = {Some remarks on the solution of linearisable second-order ordinary differential equations via point transformations},
author = {Winter Sinkala},
journal= {arXiv preprint arXiv:1904.02777},
year = {2020}
}