  The combined Einstein equations and scalar equation of motion in the
Horava-Witten scenario of the strongly coupled heterotic string compactified on
a Calabi-Yau manifold are solved in the presence of additional matter densities
on the branes. We take into account the universal Calabi-Yau modulus phi with
potentials in the 5-d bulk and on the 3-branes, and allow for an arbitrary
coupling of the additional matter to phi and an arbitrary equation of state. No
ad hoc stabilization of the five dimensional radius is assumed. The matter
densities are assumed to be small compared to the potential for phi on the
branes; in this approximation we find solutions in the bulk which are exact in
y and t. Depending on the coupling of the matter to phi and its equation of
state, various solutions for the metric on the branes and in the 5-d bulk are
obtained: Solutions corresponding to a ``rolling radius'', and solutions with a
static 5-d radius, which reproduce the standard cosmological evolution.
