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On discrete-group analysis of ordinary differential equations. (English. Russian original) Zbl 0794.58038

Sov. Math., Dokl. 37, No. 2, 403-406 (1988); translation from Dokl. Akad. Nauk SSSR 299, No. 3, 542-545 (1988).
Application of discrete groups of transformations to investigation of ordinary differential equations is discussed in this paper. In particular, maximal discrete groups of point transformations and maximal discrete groups of special nonlocal transformations for some classes of equations of the form \(y''= Ax^ n y^ m (y')^ l\) are presented; the general solution of the equation \(y''= Ax^{-15/8} y(y')^{1/2}\) is found with the help of the transformations of these groups.

MSC:

37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
54H15 Transformation groups and semigroups (topological aspects)
57S25 Groups acting on specific manifolds
34A05 Explicit solutions, first integrals of ordinary differential equations
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