Some Remarks on the Solution of Linearisable Second-Order Ordinary Differential Equations via Point Transformations

Winter Sinkala and Ji Gao

Journal of Mathematics, 2020, vol. 2020, 1-5

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.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:2406961

DOI: 10.1155/2020/2406961

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