Abel differential equations admitting a certain first integral
type: Item
instance of: scholarly article
title: Abel differential equations admitting a certain first integral
zbMATH Open document ID: 1202.34006
author: Jaume Giné
author: Xavier Santallusia
published in: Journal of Mathematical Analysis and Applications
publication date: 2010-07-20T00:00:00Z
review text: Abel differential equations in the form \[ \frac{dy}{dx}=a(x)y^3+b(x)y^2+c(x)y+d(x) \] are investigated in the present work. Conditions to have a certain first integral are given and these conditions establishing a bridge with Galois theory. The paper ends with two examples.
reviewed by: Gheorghe Tigan
Mathematics Subject Classification ID: 34A05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 5757947
zbMATH Keywords: first integral
zbMATH Keywords: Abel equation
zbMATH Keywords: Chini equation
zbMATH Keywords: classical Galois theory
MaRDI profile type: Publication
full work available at URL: j.jmaa.2010.04.046
OpenAlex ID: W2010113898
cites work: Superposition rules, Lie theorem, and partial differential equations
cites work: On the integrability of two-dimensional flows
cites work: Darboux integrability and the inverse integrating factor.
cites work: Abel ODEs: Equivalence and integrable classes
cites work: Analytic continuation and fixed points of the Poincaré mapping for a polynomial Abel equation
cites work: Q4660502
cites work: Generalized cofactors and nonlinear superposition principles
cites work: An algorithmic method to determine integrability for polynomial planar vector fields
cites work: On the integrable rational Abel differential equations
cites work: Q5784660
cites work: Q4548108
cites work: On nonlinear differential Galois theory
cites work: Q4779447
DOI: 10.1016/J.JMAA.2010.04.046
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description: scientific article; zbMATH DE number 5757947