Electron. J. Diff. Equ., Vol. 2011 (2011), No. 121, pp. 1-16.

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

Djilali Behloul, Sui Sun Cheng

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.

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Djilali Behloul
Faculté Génie Electrique
Département informatique, USTHB, BP32
El Alia, Bab Ezzouar, 16111, Algiers, Algeria
email: dbehloul@yahoo.fr
Sui Sun Cheng
Department of Mathematics, Hua University
Hsinchu 30043, Taiwan
email: sscheng@math.nthu.edu.tw

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