General Solutions of the Second-Kind Abel Equation

2025/12/18 by Ji-Xiang Zhao, Zhao, Ji-Xiang
Mathematics · Physics and Astronomy · #34A05 #34A25 #34A34 #FOS: Mathematics #Fractional Differential Equations Solutions #General Mathematics (math.GM) #Nonlinear Differential Equations Analysis #Nonlinear Waves and Solitons

paper · doi:10.48550/arxiv.2512.20656

openalex publication_date 2025/12/18 · openalex created_date 2025/12/26 · openalex updated_date 2026/07/28

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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