The Integration of Ordinary Differential Equations:
Factorization and Transformations

Lev M. Berkovich
Samara State University,
1, Acad. Pavlova Str., Samara, 443011 RUSSIA

Abstract

Necessary and sufficient conditions are found that the n-order nonlinear and nonautonomous ordinary differential equation

f(x,y,y',...,y⁽ⁿ⁾)=0

could be transformed into a linear equation with constant coefficients with the help, generally speaking, nonlocal transformations of dependent and independent variables

y=v(x,y)z, dt=u₁(x,y)dx+u₂(x,y)dy.

These conditions are expressed in termes of factorization through first order nonlinear differential operators. Examples of dynamical systems are considered also.