Rational general solutions of higher order algebraic ODEs

DOI10.1007/s11424-013-1252-0zbMath1285.34003OpenAlexW2006125674MaRDI QIDQ394458

Yan-Li Huang, Franz Winkler, Lâm Xuân Châu Ngô

Publication date: 27 January 2014

Published in: Journal of Systems Science and Complexity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11424-013-1252-0

zbMATH Keywords

algebraic ODEassociated systeminvariant algebraic space curverational first integralrational general solution

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Implicit ordinary differential equations, differential-algebraic equations (34A09) Explicit solutions, first integrals of ordinary differential equations (34A05)

Related Items

Descent of ordinary differential equations with rational general solutions ⋮ Rational general solutions of systems of first-order algebraic partial differential equations ⋮ Rational solutions of high-order algebraic ordinary differential equations ⋮ The algebro-geometric method for solving algebraic differential equations -- a survey ⋮ Unirational differential curves and differential rational parametrizations ⋮ Transforming ODEs and PDEs from radical coefficients to rational coefficients ⋮ 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

• Unnamed Item
• Unnamed Item
• Rational general solutions of first order non-autonomous parametrizable ODEs
• When does \(\langle T \rangle\) equal \(\text{sat}(T)\)?
• Rational general solutions of planar rational systems of autonomous ODEs
• On Castelnuovo's criterion of rationality P\(_a\)=P\(_2\)=0 of an algebraic surface
• Rational algebraic curves. A computer algebra approach
• Automatic parameterization of rational curves and surfaces. III: Algebraic plane curves
• Elimination methods
• Equations de Pfaff algébriques
• A new method for solving algebraic systems of positive dimension
• A generalized Euclidean algorithm for computing triangular representations of algebraic varieties
• Factorization-free decomposition algorithms in differential algebra
• On the theories of triangular sets
• The Poincaré problem in the nondicritical case
• Rational first integrals in the Darboux theory of integrability in \(\mathbb C^n\)
• A polynomial time algorithm for finding rational general solutions of first order autonomous ODEs
• Automatic parameterization of rational curves and surfaces IV: algebraic space curves
• Rational general solutions of algebraic ordinary differential equations
• Some Elementary Examples of Unirational Varieties Which are Not Rational
• Tracing index of rational curve parametrizations

This page was built for publication: Rational general solutions of higher order algebraic ODEs