A semi-algorithm to find elementary first order invariants of rational second order ordinary differential equations

Details A semi-algorithm to find elementary first order invariants of rational second order ordinary differential equations A semi-algorithm to find elementary first order invariants of rational second order ordinary differential equations

2005-06-14

arxiv.org/abs/math-ph/0506037v1

Applied Mathematics and Computation, v. 184, p. 2-11, 2007.

Physics

Mathematical Physics

Scientific paper

Here we present a method to find elementary first integrals of rational second order ordinary differential equations (SOODEs) based on a Darboux type procedure \cite{ManMac,firsTHEOps1,secondTHEOps1}. Apart from practical computational considerations, the method will be capable of telling us (up to a certain polynomial degree) if the SOODE has an elementary first integral and, in positive case, finds it via quadratures.

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