Symmetry classification of first integrals for scalar linearizable second-order ODEs

K. S. Mahomed, E. Momoniat

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

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.

Original languageEnglish
Article number847086
JournalJournal of Applied Mathematics
Volume2012
DOIs
Publication statusPublished - 2012
Externally publishedYes

ASJC Scopus subject areas

  • Applied Mathematics

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