Linearization of chazy-type third order nonlinear ordinary differential equation using the generalized Sundman transformation

Abstract

The paper studies the linearization of a Chazy-type third-order nonlinear ordinary differential equation using the Generalized Sundman Transformation (GST). Nonlinear differential equations are generally difficult to solve analytically, so transforming them into linear equations makes it easier to obtain exact solutions. The work derives the necessary conditions for GST linearization and applies them to the Chazy equation y'''+3yy''+3(y')² = 0^. By constructing suitable transformation functions, the nonlinear equation is converted into the linear third-order equation U_TTT = 0. The linear equation is then solved, and the solution of the original equation is obtained through back-substitution. Overall, the study demonstrates that the generalized Sundman transformation is an effective method for linearizing certain third-order nonlinear differential equations and obtaining their exact analytical solutions.