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2010 Exact Solutions for Certain Nonlinear Autonomous Ordinary Differential Equations of the Second Order and Families of Two-Dimensional Autonomous Systems
M. P. Markakis
Int. J. Differ. Equ. 2010: 1-13 (2010). DOI: 10.1155/2010/436860

Abstract

Certain nonlinear autonomous ordinary differential equations of the 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 the 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.

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M. P. Markakis. "Exact Solutions for Certain Nonlinear Autonomous Ordinary Differential Equations of the Second Order and Families of Two-Dimensional Autonomous Systems." Int. J. Differ. Equ. 2010 1 - 13, 2010. https://doi.org/10.1155/2010/436860

Information

Received: 19 August 2010; Revised: 22 November 2010; Accepted: 30 November 2010; Published: 2010
First available in Project Euclid: 26 January 2017

zbMATH: 1213.34006
MathSciNet: MR2746098
Digital Object Identifier: 10.1155/2010/436860

Rights: Copyright © 2010 Hindawi

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