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

Abstract EN

The necessary form of a linearizable system of two second-order ordinary differential equations y1″=f1(x,y1,y2,y1′,y2′), y2″=f2(x,y1,y2,y1′,y2′) 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.