The Integration of Ordinary Differential Equations:
Factorization and Transformations

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


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 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.


IMACS ACA'98 Electronic Proceedings