Open Access

On the Integrability of Quasihomogeneous Systems and Quasidegenerate Infinity Systems

Advances in Difference Equations20072007:098427

DOI: 10.1155/2007/98427

Received: 9 February 2007

Accepted: 21 May 2007

Published: 2 July 2007

Abstract

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.

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Authors’ Affiliations

(1)
School of Mathematics and Physics, North China Electric Power University

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Copyright

© Yanxia Hu. 2007

This article is published under license to BioMed Central Ltd. 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.