  We review O$(d,d)$ Covariant String Cosmology to all orders in $\alpha'$ in
the presence of matter and study its solutions. We show that the perturbative
analysis for a constant dilaton in the absence of a dilatonic charge does not
lead to a time-independet equation of state. Meanwhile, the non-perturbative
equations of motion allow de Sitter solutions in the String frame parametrized
by the equation of state and the dilatonic charge. Among this set of solutions,
we show that a cosmological constant equation of state implies a de Sitter
solution both in String and Einstein frames while a winding equation of state
implies a de Sitter solution in the former and a static phase in the latter. We
also consider the stability of these solutions under homogeneous linear
perturbations and show that they are not unstable, therefore defining viable
cosmological scenarios.
