On the integrable rational Abel differential equations

DOI10.1007/s00033-009-0013-3zbMath1198.34002OpenAlexW2093239577MaRDI QIDQ980683

Jaume Giné, Jaume Llibre

Publication date: 29 June 2010

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00033-009-0013-3

zbMATH Keywords

integrabilityRiccati equationAbel differential equationfirst-order linear differential equation

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Nonlinear ordinary differential equations and systems (34A34) Explicit solutions, first integrals of ordinary differential equations (34A05)

Related Items (13)

Generalized Weierstrass integrability of the Abel differential equations ⋮ Riccati-type equations associated with higher order ordinary differential equations ⋮ Derivation of the system of generalized Riccati equations from the system of evolution equations ⋮ On the planar integrable differential systems ⋮ Essential variables in the integrability problem of planar vector fields ⋮ Weierstrass integrability of complex differential equations ⋮ Representation of solutions of \(n\)-order Riccati equation via generalized trigonometric functions ⋮ Reduction of integrable planar polynomial differential systems ⋮ Center conditions and integrable forms for the Poincaré problem ⋮ Abel differential equations admitting a certain first integral ⋮ Efficient algorithms for computing rational first integrals and Darboux polynomials of planar polynomial vector fields ⋮ Weierstrass integrability for a class of differential systems ⋮ Generalized Weierstrass integrability for the complex differential equations \(\frac{dy}{dx}=a(x)y^4+b(x)y^3+c(x)y^2+d(x)y+e(x)\)

Cites Work

• A family of isochronous foci with Darboux first integral
• On the integrability of two-dimensional flows
• Darboux integrability and the inverse integrating factor.
• Integrability and algebraic limit cycles for polynomial differential systems with homogeneous nonlinearities.
• Abel ODEs: Equivalence and integrable classes
• Integrability, degenerate centers, and limit cycles for a class of polynomial differential systems
• An Abel ordinary differential equation class generalizing known integrable classes
• Orbital Linearization in the Quadratic Lotka–Volterra Systems Around Singular Points Via Lie Symmetries
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