T. Harko, __F. S. N. Lobo__, M. K. Mak

**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.

**Keywords**

first: kind: Abel: differential: equation - generalized: Abel: differential: equation - Riccati: equation - integrability: conditions; exact: solutions

**Universal Journal of Applied Mathematics**

Volume 1, Page 101

2013 October