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

J. Avellar·L. G. S. Duarte·S. E. S. Duarte·L. A. C. P. da Mota
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Abstract

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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J. Avellar, L. G. S. Duarte, S. E. S. Duarte, L. A. C. P. da Mota. 2005-06-14. A semi-algorithm to find elementary first order invariants of rational second order ordinary differential equations. https://arxiv.org/abs/math-ph/0506037

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