Solutions of some second order ODEs by the extended Prelle-Singer method and symmetrics
Anindya Ghose Choudhury, Partha Guha, and Barun Khanra
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Submission date: 28. Jul. 2008 (revised version: July 2009)
published in: Journal of nonlinear mathematical physics, 15 (2008) 4, p. 365-382
DOI number (of the published article): 10.2991/jnmp.2008.15.4.2
MSC-Numbers: 34A05, 34C99
Keywords and phrases: Prelle-Singer, Darboux polynomial, first integral
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In this paper we compute first integrals of nonlinear ordinary differential equations using the extended Prelle-Singer method, as formulated by Chandrasekar et al in J. Math. Phys. 47 (2), 023508, (2006). We find a new first integral for the Painlevé-Gambier XXII equation. We also derive the first integrals of generalized two-dimensional Kepler system and the Liénard type oscillators.