Factorization and transformations of linear and nonlinear ordinary differential equations

The monograph (Factorization and Transformation of Differential Equations: Methods and Applications, in: Regular & Chaotic Dynamics, Moscow, 2002 (in Russian)) (see also (Programming and Comput. Software 1 (2000) 25, Math. Comput. Simulation 57 (2001) 175)) by the high-skilled author presents the methods for factorization, autonomization, and exact linearization of linear and nonlinear nonautonomous ordinary differential equations of the order n, reduced to linear equations with constant coefficients of the order n. For the second-order equations, the algorithmic procedures are developed. As to linear second-order equations, the appropriate algorithms search for transformations, factorizations, and Liouvillian solutions in the system computer algebra REDUCE in the program SOLDE (see, for example, URL: http://www.ssu.samara.ru/~berkovich/ (Demo)). The present note discusses the second-order equations.