Linearization Of Nonlinear Sixth-Order Differential Equation By Generalized Sundman Transformation

Abstract

In this study, we present the linearization problem of sixth-order ordinary differential equation under the generalized Sundman transformation   X=F(t,x) dt=G(t,x)dt. We found the necessary and sufficient conditions which allow the sixth-order ordinary differential equation, x^6 to be transformed to X^6(T)=0. The process of getting the linearizing transformation is constructed proportionally and explicitly. Some examples of linearizable equation are provided to demonstrate our procedure.