  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. 
New exact cosmologies on the brane