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Linearization of coupled second order nonlinear ordinary differentialequations (SNODEs) is one of the open and challenging problems in the theory ofdifferential equations. In this paper we describe a simple and straightforwardmethod to derive linearizing transformations for a class of two coupled SNODEs.Our procedure gives several new types of linearizing transformations of bothinvertible and non-invertible kinds. In both the cases we provide algorithms toderive the general solution of the given SNODE. We illustrate the theory withpotentially important examples.

proceedings - royal society. mathematical, physical and engineering sciences

On the complete integrability and linearization of nonlinear ordinary  differential equations - Part V: Linearization of coupled second order  equations