The goal of this paper is to extend the classical Darboux theory of integrability
from autonomous polynomial vector fields to a class of nonautonomous vector
fields. We also provide sufficient conditions for applying this theory of integrability
and we illustrate this theory in several examples.
Llibre, J.; Pantazi, C. Darboux theory of integrability for a class of nonautonomous vector fields. "Journal of mathematical physics", Octubre 2009, vol. 50, núm. 102705, p. 1-19.