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On the Integrability of Quasihomogeneous Systems and Quasidegenerate Infinity Systems

Advances in Difference Equations volume 2007, Article number: 098427 (2007) Cite this article

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 and Affiliations

  1. School of Mathematics and Physics, North China Electric Power University, Beijing, 102206, China

    Yanxia Hu

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  1. Yanxia Hu
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Correspondence to Yanxia Hu.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Hu, Y. On the Integrability of Quasihomogeneous Systems and Quasidegenerate Infinity Systems. Adv Differ Equ 2007, 098427 (2007). https://doi.org/10.1155/2007/98427

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