Finding Liouvillian First Integrals of Rational ODEs of Any Order in Finite Terms

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2006
• 1. Verfasser: Kosovtsov, Y.N.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2006
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/146113
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: Finding Liouvillian First Integrals of Rational ODEs of Any Order in Finite Terms / Y.N. Kosovtsov // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 22 назв. — англ.

It is known, due to Mordukhai-Boltovski, Ritt, Prelle, Singer, Christopher and others, that if a given rational ODE has a Liouvillian first integral then the corresponding integrating factor of the ODE must be of a very special form of a product of powers and exponents of irreducible polynomials. Th...