General Solutions of the Abel Differential Equations
Exactly Solvable and Integrable Systems
2025-11-14 v7
Abstract
The Abel differential equations play a significant role in various fields of mathematics and applied sciences and are classified into two types: the first kind and the second kind. A novel derivative condition for the general solution of first-kind Abel equation is introduced. Based on this condition, the general solutions to the first-kind Abel equation with a zero free term are obtained, which in turn enables the derivation of the general solutions to the second-kind Abel equation, and meanwhile, a pair of entangled functions is discovered. These results can be extended to the Lienard equation.
Keywords
Cite
@article{arxiv.2011.10523,
title = {General Solutions of the Abel Differential Equations},
author = {Ji-Xiang Zhao},
journal= {arXiv preprint arXiv:2011.10523},
year = {2025}
}
Comments
The errors in the previous version have been corrected