Deciding the existence of rational general solutions for first-order algebraic ODEs

DOI10.1016/j.jsc.2017.06.003zbMath1390.34007OpenAlexW2728218654MaRDI QIDQ1690785

Georg Grasegger, Franz Winkler, N. Thieu Vo

Publication date: 12 January 2018

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

Full work available at URL: https://doi.org/10.1016/j.jsc.2017.06.003

zbMATH Keywords

ordinary differential equationalgebraic curverational parametrizationrational general solution

Mathematics Subject Classification ID

Rational and ruled surfaces (14J26) Geometric methods in ordinary differential equations (34A26) Nonlinear ordinary differential equations and systems (34A34) Explicit solutions, first integrals of ordinary differential equations (34A05) Special algebraic curves and curves of low genus (14H45)

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 ⋮ Möbius transformations on algebraic ODEs of order one and algebraic general solutions of the autonomous equivalence classes ⋮ Unnamed Item ⋮ Factorization of complex analytic functions algebraically dependent on space curves and applications to compatible functional and differential equations ⋮ Rational solutions of first order algebraic ordinary differential equations ⋮ Rational solutions of high-order algebraic ordinary differential equations ⋮ The algebro-geometric method for solving algebraic differential equations -- a survey ⋮ Algebraic properties of Э-functions ⋮ Existence and convergence of Puiseux series solutions for autonomous first order differential equations ⋮ Rational solutions of first-order algebraic ordinary difference equations ⋮ Solving first order autonomous algebraic ordinary differential equations by places

Uses Software

• CASA

Cites Work

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