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

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.