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Solutions of some second order ODEs by the extended Prelle-Singer method and symmetrics
Anindya Ghose Choudhury, Partha Guha and Barun KhanraAbstract
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.
- Received:
- 28.07.08
- Published:
- 24.07.09
- MSC Codes:
- 34A05, 34C99
- Keywords:
- Prelle-Singer, Darboux polynomial, first integral