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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

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.

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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Faculdade de Ciências da Universidade de Lisboa Universidade do Porto Faculdade de Ciências e Tecnologia da Universidade de Coimbra
Fundação para a Ciência e a Tecnologia COMPETE 2020 PORTUGAL 2020 União Europeia