Electron. J. Diff. Eqns., Vol. 1999(1999), No. 49, pp. 1-7.

Liouvillian first integrals of second order polynomial differential equations

Colin Christopher

We consider polynomial differential systems in the plane with Liouvillian first integrals. It is shown that all such systems have Darbouxian integrating factors, and that the search for such integrals can be reduced to a search for the invariant algebraic curves of the system and their `degenerate' counterparts.

Submitted September 7, 1999. Published December 7, 1999.
Math Subject Classifications: 34A05, 34C99.
Key Words: first integral, integrating factor, Liouville, Darboux.

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Colin Christopher
School of Mathematics and Statistics
University of Plymouth, PL4 8AA, UK
e-mail: C.Christopher@plymouth.ac.uk

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