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.