Table of Contents
ISRN Mathematical Analysis
Volume 2011 (2011), Article ID 452689, 21 pages
http://dx.doi.org/10.5402/2011/452689
Research Article

Linearization of Two Second-Order Ordinary Differential Equations via Fiber Preserving Point Transformations

School of Mathematics, Institute of Science, Suranaree University of Technology, Nakhon Ratchasima 30000, Thailand

Received 1 July 2011; Accepted 4 August 2011

Academic Editor: M. Escobedo

Copyright Β© 2011 Sakka Sookmee and Sergey V. Meleshko. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The necessary form of a linearizable system of two second-order ordinary differential equations 𝑦1ξ…žξ…ž=𝑓1(π‘₯,𝑦1,𝑦2,π‘¦ξ…ž1,π‘¦ξ…ž2), 𝑦2ξ…žξ…ž=𝑓2(π‘₯,𝑦1,𝑦2,π‘¦ξ…ž1,π‘¦ξ…ž2) is obtained. Some other necessary conditions were also found. The main problem studied in the paper is to obtain criteria for a system to be equivalent to a linear system with constant coefficients under fiber preserving transformations. A linear system with constant coefficients is chosen because of its simplicity in finding the general solution. Examples demonstrating the procedure of using the linearization theorems are presented.