We study the Liouvillian first integrals for the generalized Liénard polynomial differential systems of the form x′ = y, y′ = -g(x) - f(x)y, where g(x) and f(x) are arbitrary polynomials such that 2 ≤ deg g ≤ deg f.
- Darboux polynomial
- Exponential factor
- Generalized Liénard polynomial differential system
- Liouvillian first integral