We characterize the Liouvillian first integrals for the Liénard polynomial differential systems of the form x′ = y, y′ = -cx - f(x)y, with c ∈ ℝ and f(x) is an arbitrary polynomial. For obtaining this result we need to find all the Darboux polynomials and the exponential factors of these systems. © 2010 American Mathematical Society.
|Journal||Proceedings of the American Mathematical Society|
|Publication status||Published - 1 Sep 2010|
- Darboux polynomials
- Exponential factors
- Liénard polynomial differential systems
- Liouvillian first integrals