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Zbl 1135.34029
Mahomed, F.M.
Symmetry group classification of ordinary differential equations: Survey of some results. (English)
[J] Math. Methods Appl. Sci. 30, No. 16, 1995-2012 (2007). ISSN 0170-4214; ISSN 1099-1476/e

After the famous results of Sophus Lie on symmetry analysis of ordinary differential equations several results on point symmetry group analysis have been obtained, particularly by P. Leach. This article presents a review on the point symmetry group properties of linear $n$th order ($n\geq 1$) differential equations as well as the point symmetry group classification of scalar second order ODEs both in the real and complex domains. Many references are given to the papers of P. Leach on well-researched equations and related results on classification and integrability together with some open problem in this domain.
[O. Makeev (Ulyanovsk)]

MSC 2000:: *34C14 Symmetries, invariants
34C20 Transformation of ODE and systems
34A30 Linear ODE and systems
70H33 Symmetries

Keywords: ordinary differential equation; symmetry; transformations

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