Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 121, pp. 1-16.

Title: Computation of rational solutions for a
       first-order nonlinear differential equation

Authors: Djilali Behloul (USTHB, Algiers, Algeria)
         Sui Sun Cheng (Hua Univ., Hsinchu, Taiwan)

Abstract:
 In this article, we study  differential equations of
 the form $y'=\sum A_i(x)y^i/\sum B_i(x)y^i$ which
 can be elliptic, hyperbolic, parabolic, Riccati, or quasi-linear.
 We show how rational solutions can be computed in a systematic manner.
 Such results are most likely to find applications in the theory of
 limit cycles as indicated by Gine et al [4].

Submitted August 23, 2011. Published September 19, 2011.
Math Subject Classifications: 34A05.
Key Words: Polynomial solution; rational solution; nonlinear differential 
           equation.