Linearisable third order ordinary differential equations and generalised Sundman transformations

TL;DR

This paper investigates the conditions under which third order ordinary differential equations can be linearized using generalized Sundman transformations, extending the theory to more general cases.

Contribution

It provides detailed conditions for linearizing third order ODEs via generalized Sundman transformations and explores further generalizations.

Findings

Derived explicit conditions for linearizability of third order ODEs.

Extended the linearization framework to more general transformations.

Enhanced understanding of the structure of third order ODEs under transformations.

Abstract

We calculate in detail the conditions which allow the most general third order ordinary differential equation to be linearised in X'''(T)=0 under the transformation X(T)=F(x,t), dT=G(x,t)dt. Further generalisations are considered.