Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Abel ordinary differential equation class generalizing known
  integrable classes   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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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: alg-geom