  We develop a method for constructing exact cosmological solutions in brane
world cosmology. New classes of cosmological solutions on Randall-Sandrum brane
are obtained. The superpotential and Hubble parameter are represented in
quadratures. These solutions have inflationary phases under general assumptions
and also describe an exit from the inflationary phase without a fine tuning of
the parameters. Another class solutions can describe the current phase of
accelerated expansion with or without possible exit from it.
