Abstract. In this letter, we introduce a new generalized linearizing transformation (GLT) for second-order nonlinear ordinary differential equations (SNODEs). The well-known invertible point (IPT) and non-point transformations (NPT) can be derived as sub-cases of the GLT. A wider class of nonlinear ODEs that cannot be linearized through NPT and IPT can be linearized by this GLT. We also illustrate how to construct GLTs and to identify the form of the linearizable equations and propose a procedure to derive the general solution from this GLT for the SNODEs. We demonstrate the theory with two examples which are of contemporary interest.

PACS numbers: 02.30.Hq, 05.45.−a

Print publication: Issue 3 (20 January 2006)
Received 18 October 2005, in final form 25 November 2005
Published 21 December 2005