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arXiv · 2011.10523

General Solutions of the Abel Differential Equations

Ji-Xiang Zhao
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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.

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Ji-Xiang Zhao. 2020-11-19. General Solutions of the Abel Differential Equations. https://arxiv.org/abs/2011.10523

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