Conditional linearizability criteria for a system of third-order ordinary differential equations

TL;DR

This paper develops criteria for linearizing a specific class of third-order ODE systems by differentiating second-order systems, with detailed analysis for constant and variable coefficient cases, including examples.

Contribution

It introduces a novel method to determine linearizability of third-order ODE systems based on second-order system differentiation and case-specific analysis.

Findings

Linearizability criteria established for third-order ODE systems

Method applicable to systems with constant and variable coefficients

Examples demonstrate the criteria's practical use

Abstract

We provide linearizability criteria for a class of systems of third-order ordinary differential equations (ODEs) that is cubically semi-linear in the first derivative, by differentiating a system of second-order quadratically semi-linear ODEs and using the original system to replace the second derivative. The procedure developed splits into two cases, those where the coefficients are constant and those where they are variables. Both cases are discussed and examples given.