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arXiv · 2405.07912

A Linear Prelle-Singer method

L. G. S. Duarte·H. S. Ferreira·L. A. C. P. da Mota
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Abstract

The Prelle-Singer method allows determining an elementary first integral admitted by a polynomial vector field in the plane. It is a semi-algorithm whose nonlinear step consists of determining the Darboux polynomials of the vector field. In this article we construct a linear procedure to determine the Darboux polynomials present in the integrating factor of a polynomial vector field in the plane. Next, we extend the procedure to deal with rational 2ODEs that admit an elementary first integral

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BibTeXRIS

L. G. S. Duarte, H. S. Ferreira, L. A. C. P. da Mota. 2024-05-13. A Linear Prelle-Singer method. https://arxiv.org/abs/2405.07912

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