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.
"On the Equivalence of Differential Equations in the Sense of Coincidence Reflecting Functions." Abstr. Appl. Anal. 2015 1 - 8, 2015. https://doi.org/10.1155/2015/456364