The method of an exact linearization of n-order ordinary differential equations

Abstract

Necessary and sufficient conditions are found that the n-order nonlinear and nonautonomous ordinary differential equation could be transformed into a linear equation with constant coefficients with the help, generally speaking, nonlocal transformation of dependent and independent variables. These conditions are expressed in termes of factorization through first order nonlinear differential operators. Examples are considered also. “Two subjects that are theoretical physics and integration of differential equations, are quitely impossible one without another, were always developing together, and the success of one of them influenced another” (V.P. Ermakov). © 1996 Taylor & Francis Group, LLC.