An Abel ordinary differential equation class generalizing known integrable classes

Details An Abel ordinary differential equation class generalizing known integrable classes An Abel ordinary differential equation class generalizing known integrable classes

2000-02-08

arxiv.org/abs/math/0002059v3

European Journal of Applied Mathematics (2003), vol. 14, pp. 217-229

Mathematics

General Mathematics

11 pages. Original version: Aug/1999. Related Maple programs for Abel ODEs are available at http://lie.uwaterloo.ca/odetools.h

Scientific paper

We present a multi-parameter non-constant-invariant class of Abel ordinary differential equations with the following remarkable features. This one class is shown to unify, that is, contain as particular cases, all the integrable classes presented by Abel, Liouville and Appell, as well as all those shown in Kamke's book and various other references. In addition, the class being presented includes other new and fully integrable subclasses, as well as the most general parameterized class of which we know whose members can systematically be mapped into Riccati equations. Finally, many integrable members of this class can be systematically mapped into an integrable member of a different class. We thus find new integrable classes from previously known ones.

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