Linearizability Criteria for a Class of Third Order Semi-Linear ODEs

TL;DR

This paper develops new geometric criteria for linearizing a specific class of third order semi-linear ordinary differential equations by extending methods used for second order equations, providing novel insights beyond existing literature.

Contribution

It introduces a new approach to linearize third order semi-linear ODEs by extending second order geometric methods, offering criteria not previously available.

Findings

Derived linearizability criteria for third order semi-linear ODEs

Extended second order geometric linearization methods to third order

Provided illustrative examples demonstrating the criteria

Abstract

Using geometric methods for linearizing systems of second order cubically semi-linear ordinary differential equations, we extend to the third order by differentiating the second order equation. This yields criteria for linearizability of a class of third order semi-linear ordinary differential equations, which is distinct from the classes available in the literature. Some examples are given and discussed.