On the Equivalence of Differential Equations in the Sense of Coincidence Reflecting Functions

Abstract EN

We use a new method for constructing some differential equations which are equivalent to a given equation in the sense of having the same reflecting function.

We completely solve the problem: when is a polynomial differential equation equivalent to a given polynomial differential equation? Many sufficient conditions have been established for one differential equation to be equivalent to a given differential equation.

We apply the obtained results to study the boundary value problem of two equivalent differential equations.