  We present an exact analytical solution of the Einstein equations with
cosmological constant in a spatially flat Robertson-Walker metric. This is
interpreted as an isotropic Lemaitre-type version of the cosmological Friedmann
model. Implications in the recent discovered cosmic acceleration of the
universe and in the theory of an inflationary model of the universe are in
view. Some properties of this solution are pointed out as a result of numerical
investigations of the model.
