Exact solutions for certain nonlinear autonomous ordinary differential equations of the second order and families of two-dimensional autonomous systems
type: Item
instance of: scholarly article
title: Exact solutions for certain nonlinear autonomous ordinary differential equations of the second order and families of two-dimensional autonomous systems
zbMATH Open document ID: 1213.34006
DOI: 10.1155/2010/436860
author: Juan-Miguel Gracia
published in: International Journal of Differential Equations
publication date: 2011-03-08T00:00:00Z
full work available at URL: https://eudml.org/doc/230559
review text: Summary: Certain nonlinear autonomous ordinary differential equations of second order are reduced to Abel equations of the first kind ((Ab-1) equations). Based on the results of a previous work, concerning a closed-form solution of a general (Ab-1) equation, and introducing an arbitrary function, exact one-parameter families of solutions are derived for the original autonomous equations, for most of which only first integrals (in closed or parametric form) have been obtained so far. Two-dimensional autonomous systems of differential equations of the first order, equivalent to the considered herein autonomous forms, are constructed and solved by means of the developed analysis.
Mathematics Subject Classification ID: 34A05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 5862343
Wikidata QID: Q58651251
MaRDI profile type: Publication
OpenAlex ID: W2025881413
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description: scientific article; zbMATH DE number 5862343