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The necessary form of a linearizable system of two second-order ordinary differential equations 1=1(,1,2,1,2), 2=2(,1,2,1,2) 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.

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