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Journal of Applied Mathematics
Volume 2017, Article ID 7302081, 9 pages
https://doi.org/10.1155/2017/7302081
Research Article

First Integrals and Hamiltonians of Some Classes of ODEs of Maximal Symmetry

Department of Mathematics and Applied Mathematics, University of Venda, P/B X5050, Thohoyandou, Limpopo 0950, South Africa

Correspondence should be addressed to J. C. Ndogmo; moc.oohay@jomgodn

Received 5 December 2016; Revised 12 January 2017; Accepted 22 January 2017; Published 14 February 2017

Academic Editor: Peter G. L. Leach

Copyright © 2017 J. C. Ndogmo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Complete sets of linearly independent first integrals are found for the most general form of linear equations of maximal symmetry algebra of order ranging from two to eight. The corresponding Hamiltonian systems are constructed and it is shown that their general solutions can also be found by a simple superposition formula from the solutions of a scalar second-order source equation.