Geodesic
Liouvillian first integrals of second order polynomial differential equations
Electronic Journal of Differential Equations, Tome 1999 (1999).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 34A05, 34C99
Keywords: first integral, integrating factor, Liouville, Darboux 
@article{EJDE_1999__1999__a13,
     author = {Christopher, Colin},
     title = {Liouvillian first integrals of second order polynomial differential equations},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {1999},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a13/}
}
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Christopher, Colin. Liouvillian first integrals of second order polynomial differential equations. Electronic Journal of Differential Equations, Tome 1999 (1999). http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a13/