An O(d,d) symmetry of the manifold of string vacua that do not depend on d (out of D) space-time coordinates has been recently identified. Here we write down, for d = D - 1, the low energy equations of motion and their general solution in a manifestly O(d,d)-invariant form, pointing out an amusing similarity with the renormalization group framework. Previously considered cosmological and black hole solutions are reproduced as particular examples.