Electronic Journal of Differential Equations,
Vol. 1999(1999), No. 49, pp. 1-7.

Title: Liouvillian first integrals of second order
       polynomial differential equations

Author: Colin Christopher (Univ. of Plymouth, UK)

Abstract: 
 
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.