Equivalence of Linear Systems of Two Second-Order Ordinary Differential Equations

Abstract

An equivalence problem is solved completely for a linear system of two second-order ordinary differential equations. Using Lie's infinitesimal method we construct the basis of differential invariants for this class of equations and provide the operators of invariant differentiation. Certain types of linear systems are described in terms of their invariants. Some examples are given to illustrate our results. Key Words: Linear Equation; System of Second-Order Ordinary Differential Equations; Equivalence Problem; Differential Invariant