Rational general solutions of planar rational systems of autonomous ODEs

DOI10.1016/j.jsc.2011.06.002zbMath1235.34004OpenAlexW2064034118WikidataQ43216838 ScholiaQ43216838MaRDI QIDQ719763

Franz Winkler, Lâm Xuân Châu Ngô

Publication date: 11 October 2011

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jsc.2011.06.002

zbMATH Keywords

ordinary differential equationsrational solutionsrational parametrizationsrational first integralsinvariant algebraic curves

Mathematics Subject Classification ID

Explicit solutions, first integrals of ordinary differential equations (34A05) Invariant manifolds for ordinary differential equations (34C45)

Related Items (13)

The algebro-geometric method: Solving algebraic differential equations by parametrizations ⋮ Computation of all rational solutions of first-order algebraic ODEs ⋮ Rational Liouvillian solutions of algebraic ordinary differential equations of order one ⋮ Rational general solutions of systems of first-order algebraic partial differential equations ⋮ Rational general solutions of higher order algebraic ODEs ⋮ Möbius transformations on algebraic ODEs of order one and algebraic general solutions of the autonomous equivalence classes ⋮ Deciding the existence of rational general solutions for first-order algebraic ODEs ⋮ Rational general solutions of trivariate rational differential systems ⋮ The algebro-geometric method for solving algebraic differential equations -- a survey ⋮ Unirational differential curves and differential rational parametrizations ⋮ A solution method for autonomous first-order algebraic partial differential equations ⋮ Symbolic Solutions of First-Order Algebraic ODEs ⋮ Birational transformations preserving rational solutions of algebraic ordinary differential equations

Uses Software

• CASA

Cites Work

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• Associative differential operations
• Elementary First Integrals of Differential Equations
• Liouvillian First Integrals of Differential Equations
• Darboux integrability and invariant algebraic curves for planar polynomial systems
• Rational general solutions of algebraic ordinary differential equations
• Tracing index of rational curve parametrizations

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