Exact Solutions for Certain Nonlinear Autonomous Ordinary Differential Equations of the Second Order and Families of Two-Dimensional Autonomous Systems
نویسندگان
چکیده
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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