Advances in Difference Equations
Volume 2007 (2007), Article ID 98427, 10 pages
On the Integrability of Quasihomogeneous Systems and Quasidegenerate Infinity Systems
School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China
Received 9 February 2007; Accepted 21 May 2007
Academic Editor: Kilkothur Munirathinam Tamizhmani
Copyright © 2007 Yanxia Hu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The integrability of quasihomogeneous systems is considered, and the
properties of the first integrals and the inverse integrating factors of such systems are shown.
By solving the systems of ordinary differential equations which are established by using the vector
fields of the quasihomogeneous systems, one can obtain an inverse integrating factor of the
systems. Moreover, the integrability of a class of systems (quasidegenerate infinity systems)
which generalize the so-called degenerate infinity vector fields is considered, and a method how
to obtain an inverse integrating factor of the systems from the first integrals of the corresponding
quasihomogeneous systems is shown.