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

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

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