Exact Solutions for Certain Nonlinear Autonomous Ordinary Differential Equations of the Second Order and Families of Two-Dimensional Autonomous SystemsReport as inadecuate




Exact Solutions for Certain Nonlinear Autonomous Ordinary Differential Equations of the Second Order and Families of Two-Dimensional Autonomous Systems - Download this document for free, or read online. Document in PDF available to download.

International Journal of Differential EquationsVolume 2010 2010, Article ID 436860, 13 pages

Research ArticleDepartment of Engineering Sciences, University of Patras, 26504 Patras, Greece

Received 19 August 2010; Revised 22 November 2010; Accepted 30 November 2010

Academic Editor: Peiguang Wang

Copyright © 2010 M. P. Markakis. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.





Author: M. P. Markakis

Source: https://www.hindawi.com/



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