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Transformations of linear differential equations of second order and adjoined nonlinear equations. (English) Zbl 0914.34035

This paper is a review of results concerning transformations of linear differential equations studied by Euler, Kummer, Liouville, Lyapunov, S. Lie, Darboux, Halphen, Imshenetskii, Bohl and others. O. Bor ůvka was the first who systematically investigated the Kummer-Liouville transformation to second-order linear differential equations from the global point of view. The authors of the paper dedicated to O. Borůvka give a nice survey of related results and generalizations, including algorithmic procedures and adjoined nonlinear equations. The list of references contains fifty items, from historical works to the latest ones, some of them even not well-known.
Reviewer: F.Neuman (Brno)

MSC:

34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
34-03 History of ordinary differential equations
34A30 Linear ordinary differential equations and systems
34A05 Explicit solutions, first integrals of ordinary differential equations
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