Table of Contents
ISRN Applied Mathematics
Volume 2011, Article ID 852656, 44 pages
http://dx.doi.org/10.5402/2011/852656
Research Article

Rational Solutions of Riccati Differential Equation with Coefficients Rational

Department of Mathematics, Tunis El Manar University, Tunis 1002, Tunisia

Received 28 March 2011; Accepted 16 April 2011

Academic Editors: H.-T. Hu and X. Meng

Copyright © 2011 Nadhem Echi. 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.

Abstract

This paper presents a simple and efficient method for determining the rational solution of Riccati differential equation with coefficients rational. In case the differential Galois group of the differential equation ( 𝐸 𝑙 ) ∢ 𝑦 ξ…ž ξ…ž = π‘Ÿ 𝑦 , π‘Ÿ ∈ β„‚ ( π‘₯ ) is reducible, we look for the rational solutions of Riccati differential equation πœƒ ξ…ž + πœƒ 2 = π‘Ÿ , by reducing the number of checks to be made and by accelerating the search for the partial fraction decomposition of the solution reserved for the poles of πœƒ which are false poles of π‘Ÿ . This partial fraction decomposition of solution can be used to code π‘Ÿ . The examples demonstrate the effectiveness of the method.