  The Einstein field equations for several cosmological models reduce to
polynomial systems of ordinary differential equations. In this paper we shall
concentrate our attention to the spatially homogeneous diagonal G_2
cosmologies. By using Darboux's theory in order to study ordinary differential
equations in the complex projective plane CP^2 we solve the Bianchi V models
totally. Moreover, we carry out a study of Bianchi VI models and first
integrals are given in particular cases.
