Computation of all rational solutions of first-order algebraic ODEs

DOI10.1016/j.aam.2018.03.002zbMath1393.34008OpenAlexW2792012667MaRDI QIDQ1647939

Thieu N. Vo, Franz Winkler, Georg Grasegger

Publication date: 27 June 2018

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aam.2018.03.002

zbMATH Keywords

ordinary differential equationrational curverational solutionalgebraic function field

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Implicit ordinary differential equations, differential-algebraic equations (34A09) Explicit solutions, first integrals of ordinary differential equations (34A05) Special algebraic curves and curves of low genus (14H45)

Related Items (8)

Descent of ordinary differential equations with rational general solutions ⋮ Transcendental Liouvillian solutions of first order nonlinear 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 ⋮ Transforming ODEs and PDEs from radical coefficients to rational coefficients ⋮ Rational solutions of first-order algebraic ordinary difference equations

Uses Software

• CASA

Cites Work

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• First order algebraic differential equations. A differential algebraic approach
• Deciding the existence of rational general solutions for first-order algebraic ODEs
• The Poincaré problem in the nondicritical case
• A polynomial time algorithm for finding rational general solutions of first order autonomous ODEs
• Symbolic Solutions of First-Order Algebraic ODEs
• Algebraic General Solutions of First Order Algebraic ODEs
• Rational general solutions of algebraic ordinary differential equations

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