Liouvillian First Integrals for Generalized Liénard Polynomial Differential Systems

Abstract

We study the Liouvillian first integrals for the generalized Liénard polynomial differential systems of the form xʹ = y, yʹ = -g(x) - f(x)y, where g(x) and f(x) are arbitrary polynomials such that 2 ≤ deg g ≤ deg f.