Abstract
In Cheb-Terrab and Roche (Comput Phys Commun 130(1–2):204–231, 2000) a classification of the Abel equations known as solvable in the literature was presented. In this paper, we show that all the integrable rational Abel differential equations that appear in Cheb-Terrab and Roche (Comput Phys Commun 130(1–2):204–231, 2000) and consequently in Cheb-Terrab and Roche (Eur J Appl Math 14(2):217–229, 2003) can be reduced to a Riccati differential equation or to a first-order linear differential equation through a change with a rational map. The change is given explicitly for each class. Moreover, we have found a unified way to find the rational map from the knowledge of the explicitly first integral.
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J. Giné is partially supported by a MCYT/FEDER grant number MTM2008-00694 and by a CIRIT grant number 2005SGR 00550.
J. Llibre is partially supported by a MCYT/FEDER grant number MTM2008-03437 and by a CIRIT grant number 2005SGR 00550.
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Giné, J., Llibre, J. On the integrable rational Abel differential equations. Z. Angew. Math. Phys. 61, 33–39 (2010). https://doi.org/10.1007/s00033-009-0013-3
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DOI: https://doi.org/10.1007/s00033-009-0013-3