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arXiv · 1310.1508

A Chiellini type integrability condition for the generalized first kind Abel differential equation

Tiberiu Harko·Francisco S. N. Lobo·M. K. Mak
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Abstract

The Chiellini integrability condition of the first order first kind Abel equation $dy/dx=f(x)y^2+g(x)y^3$ is extended to the case of the general Abel equation of the form $dy/dx=a(x)+b(x)y+f(x)y^{\alpha -1}+g(x)y^{\alpha}$, where $\alpha \in \Re$, and $\alpha > 1$. In the case $\alpha =2$ the generalized Abel equations reduces to a Riccati type equation, for which a Chiellini type integrability condition is obtained.

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Tiberiu Harko, Francisco S. N. Lobo, M. K. Mak. 2013-10-05. A Chiellini type integrability condition for the generalized first kind Abel differential equation. https://doi.org/10.13189/ujam.2013.010209

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