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\centerline{\bf Three Methods for Exact Integration of ODEs Compared}

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\centerline{Alexei Bocharov}
\centerline{Wolfram Research Inc.}
\centerline{Champaign, IL 61820, USA}
\centerline{alexei@wolfram.com, alexeib@ACM.org}

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The talk gives an overview of three computer algebra methods for finding
exact  closed form solutions of ordinary differential equations. Two
general  methods  covered are those based on symmetry analysis and
equivalence problem approach.  A short analysis  of  Prelle-Singer
procedure for the first-order ODEs is also done.   Conceptual and
practical comparisons of the methods are performed whenever possible.
In particular, for the class of equations solved by symmetry analysis
and class of equations solvable by Prelle-Singer procedure, the
intersection and difference of these classes is outlined based both on
theoretical observations and on test results.

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