TITLE:
Linearization of Emden Differential Equation via the Generalized Sundman Transformations
AUTHORS:
Joel Mvendaga Orverem, Yusuf Haruna, Bala Ma’aji Abdulhamid, Magaji Yunbunga Adamu
KEYWORDS:
Emden Differential Equation, Second Order, Ordinary Differential Equation, Generalized Sundman Transformation, Linearization
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.11 No.3,
March
12,
2021
ABSTRACT: The Emden differential equation is one of the most widely studied and challenging nonlinear dynamics equations in literature. It finds applications in various areas of study such as celestial mechanics, fluid mechanics, Steller structure, isothermal gas spheres, thermionic currents and so on. Because of the importance of the equation, the method of generalized Sundman transformation (GST) as proposed by Nakpim and Meleshko is used for linearizing the Emden differential equation. The Emden differential equation considered here is a modification of the equation given by Berkovic. The results obtained in this paper imply that the Emden equation cannot be linearized by a point transformation. The general solution of the modified Emden equation is also obtained.