General Solutions of the Second-Kind Abel Equation
Ji-Xiang Zhao
TL;DR
This paper presents the first general solutions with free variables for the long-unsolved second-kind Abel equation using an elementary quadrature method.
Contribution
It introduces a novel elementary quadrature approach to solve the second-kind Abel equation, providing the first general solutions with free variables.
Findings
First general solutions with free variables derived
Solution method is elementary and straightforward
Addresses a nearly two-century-old mathematical problem
Abstract
The general solutions with free variable to the second-kind Abel equation, a nonlinear ordinary differential equation that has remained unsolved for nearly two centuries, are presented for the first time by using elementary quadrature method.
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Taxonomy
TopicsNonlinear Waves and Solitons · Fractional Differential Equations Solutions · Nonlinear Differential Equations Analysis