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

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

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Instituto de Astrofísica e Ciências do Espaço Universidade do Porto Faculdade de Ciências da Universidade de Lisboa Fundação para a Ciência e a Tecnologia
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