Abel ODEs: Equivalence and Integrable Classes

Abstract

A classification, according to invariant theory, of non-constant invariant Abel ODEs known as solvable and found in the literature is presented. A set of new integrable classes depending on one or no parameters, derived from the analysis of the works by Abel, Liouville and Appell, is also shown. Computer algebra routines were developed to solve ODEs members of these classes by solving their related equivalence problem. The resulting library permits a systematic solving of Abel type ODEs in the Maple symbolic computing environment.

31 pages; accepted (Jan/2000) for publication in Computer Physics Communications. Related maple programs for Abel ODEs together with the ODEtools package are available at http://lie.uwaterloo.ca/odetools.htm

References in corpus (2)

• Computer Algebra Solving of First Order ODEs Using Symmetry Methods
• Computer Algebra Solving of Second Order ODEs Using Symmetry Methods

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