Method of factorization of ordinary differential operators and some of its applications

The paper is dedicated to analytical and algebraic approaches to the problem of the integration of ordinary differential equations. The first part is devoted to linear ordinary differential equations of the second and nth orders, while the second deals with nonlinear ordinary differential equations. Factorization of nonlinear equations of the second and the third orders both through commutative and noncommutative nonlinear differential operators are considered. The method of the exact linearization for nonlinear equations is explained. Some applications are also considered.