Cosmological consequences of adding the Cold Dark Matter (CDM) to the exactly solvable stringy Dark Energy (DE) model are investigated. The model is motivated by the consideration of our Universe as a slowly decaying D3-brane. The decay of this D-brane is described in the String Field Theory framework. Stability conditions of the exact solution with respect to small fluctuations of the initial value of the CDM energy density are found. Solutions with large initial value of the CDM energy density attracted by the exact solution without CDM are constructed numerically. In contrast to the LambdaCDM model the Hubble parameter in the model is not a monotonic function of time. For specific initial data the DE state parameter w_{DE} is also not monotonic function of time. For these cases there are two separate regions of time where w_{DE} being less than -1 is close to -1.

15 pages, 6 figures; references added