Geodesic
A simple method for constructing non-liouvillian first integrals of autonomous planar systems
Czechoslovak Mathematical Journal, Tome 56 (2006) no. 3, pp. 987-999 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We show that a transformation method relating planar first-order differential systems to second order equations is an effective tool for finding non-liouvillian first integrals. We obtain explicit first integrals for a subclass of Kukles systems, including fourth and fifth order systems, and for generalized Liénard-type systems.
We show that a transformation method relating planar first-order differential systems to second order equations is an effective tool for finding non-liouvillian first integrals. We obtain explicit first integrals for a subclass of Kukles systems, including fourth and fifth order systems, and for generalized Liénard-type systems.
Classification : 33C99, 34A25, 34C07, 34C14, 81U15
Keywords: planar polynomial systems; Kukles systems; generalized Liénard systems; non-liouvillian first integrals 
@article{CMJ_2006_56_3_a17,
     author = {Schulze-Halberg, Axel},
     title = {A simple method for constructing non-liouvillian first integrals of autonomous planar systems},
     journal = {Czechoslovak Mathematical Journal},
     pages = {987--999},
     year = {2006},
     volume = {56},
     number = {3},
     mrnumber = {2261671},
     zbl = {1164.34396},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2006_56_3_a17/}
}
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Schulze-Halberg, Axel. A simple method for constructing non-liouvillian first integrals of autonomous planar systems. Czechoslovak Mathematical Journal, Tome 56 (2006) no. 3, pp. 987-999. http://geodesic.mathdoc.fr/item/CMJ_2006_56_3_a17/