Algorithmic Reduction and Rational General Solutions of First Order Algebraic Differential Equations

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dc.creatorChen, Guoting
dc.creatorMa, Yujie
dc.date2005-05-14
dc.date.accessioned2026-07-07T05:19:53Z
dc.date.available2026-07-07T05:19:53Z
dc.descriptionFirst order algebraic differential equations are considered. An necessary condition for a first order algebraic differential equation to have a rational general solution is given: the algebraic genus of the equation should be zero. Combining with Fuchs' conditions for algebraic differential equations without movable critical point, an algorithm is given for the computation of rational general solutions of these equations if they exist under the assumption that a rational parametrization is provided. It is based on an algorithmic reduction of first order algebraic differential equations with algebraic genus zero and without movable critical point to classical Riccati equations.
dc.identifierhttps://arxiv.org/abs/math/0505299
dc.identifierhttp://arxiv.org/abs/math/0505299
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75192
dc.subjectClassical Analysis and ODEs
dc.subjectComplex Variables
dc.subjectPrimary 34A09, 68W30; Secondary 14Q05, 34M15
dc.titleAlgorithmic Reduction and Rational General Solutions of First Order Algebraic Differential Equations
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