  The D-dimensional cosmological model on the manifold $M = R \times M_{1}
\times M_{2}$ describing the evolution of 2 Einsteinian factor spaces, $M_1$
and $M_2$, in the presence of multicomponent perfect fluid source is
considered. The barotropic equation of state for mass-energy densities and the
pressures of the components is assumed in each space. When the number of the
non Ricci-flat factor spaces and the number of the perfect fluid components are
both equal to 2, the Einstein equations for the model are reduced to the
generalized Emden-Fowler (second-order ordinary differential) equation, which
has been recently investigated by Zaitsev and Polyanin within discrete-group
analysis. Using the integrable classes of this equation one generates the
integrable cosmological models. The corresponding metrics are presented. The
method is demonstrated for the special model with Ricci-flat spaces $M_1,M_2$
and the 2-component perfect fluid source.
