  In this paper, we present a real non-linear differential equation for the two
flavor neutrino oscillation problem in matter with an arbitrary density
profile. We also present an exact series solution to this non-linear
differential equation. In addition, we investigate numerically the convergence
of this solution for different matter density profiles such as constant and
linear profiles as well as the Preliminary Reference Earth Model describing the
Earth's matter density profile. Finally, we discuss other methods used for
solving the neutrino flavor evolution problem.
