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Exact Solutions for Certain Nonlinear Autonomous Ordinary Differential Equations of the Second Order and Families of Two-Dimensional Autonomous Systems
Author
Source
International Journal of Differential Equations
Issue
Vol. 2010, Issue 2010 (31 Dec. 2010), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2010-12-20
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Markakis, M. P.. 2010. Exact Solutions for Certain Nonlinear Autonomous Ordinary Differential Equations of the Second Order and Families of Two-Dimensional Autonomous Systems. International Journal of Differential Equations،Vol. 2010, no. 2010, pp.1-13.
https://search.emarefa.net/detail/BIM-472185
Modern Language Association (MLA)
Markakis, M. P.. Exact Solutions for Certain Nonlinear Autonomous Ordinary Differential Equations of the Second Order and Families of Two-Dimensional Autonomous Systems. International Journal of Differential Equations No. 2010 (2010), pp.1-13.
https://search.emarefa.net/detail/BIM-472185
American Medical Association (AMA)
Markakis, M. P.. Exact Solutions for Certain Nonlinear Autonomous Ordinary Differential Equations of the Second Order and Families of Two-Dimensional Autonomous Systems. International Journal of Differential Equations. 2010. Vol. 2010, no. 2010, pp.1-13.
https://search.emarefa.net/detail/BIM-472185
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-472185