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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 isconsidered. The barotropic equation of state for mass-energy densities and thepressures of the components is assumed in each space. When the number of thenon Ricci-flat factor spaces and the number of the perfect fluid components areboth equal to 2, the Einstein equations for the model are reduced to thegeneralized Emden-Fowler (second-order ordinary differential) equation, whichhas been recently investigated by Zaitsev and Polyanin within discrete-groupanalysis. Using the integrable classes of this equation one generates theintegrable cosmological models. The corresponding metrics are presented. Themethod is demonstrated for the special model with Ricci-flat spaces $M_1,M_2$and the 2-component perfect fluid source.Comment: LaTeX file, no figure

Integration ofD-dimensional cosmological models with two factor spaces by reduction to the generalized Emden-Fowler equation