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2012 Symmetry Classification of First Integrals for Scalar Linearizable Second-Order ODEs
K. S. Mahomed, E. Momoniat
J. Appl. Math. 2012(SI14): 1-14 (2012). DOI: 10.1155/2012/847086

Abstract

Symmetries of the fundamental first integrals for scalar second-order ordinary differential equations (ODEs) which are linear or linearizable by point transformations have already been obtained. Firstly we show how one can determine the relationship between the symmetries and the first integrals of linear or linearizable scalar ODEs of order two. Secondly, a complete classification of point symmetries of first integrals of such linear ODEs is studied. As a consequence, we provide a counting theorem for the point symmetries of first integrals of scalar linearizable second-order ODEs. We show that there exists the 0-, 1-, 2-, or 3-point symmetry cases. It is shown that the maximal algebra case is unique.

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K. S. Mahomed. E. Momoniat. "Symmetry Classification of First Integrals for Scalar Linearizable Second-Order ODEs." J. Appl. Math. 2012 (SI14) 1 - 14, 2012. https://doi.org/10.1155/2012/847086

Information

Published: 2012
First available in Project Euclid: 3 January 2013

zbMATH: 1272.34046
MathSciNet: MR2997240
Digital Object Identifier: 10.1155/2012/847086

Rights: Copyright © 2012 Hindawi

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Vol.2012 • No. SI14 • 2012
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