  The problem of a non-steady planar radiation mediated shock (RMS) breaking
out from a surface with a power-law density profile, \rho\propto x^n, is
numerically solved in the approximation of diffusion with constant opacity. For
an appropriate choice of time, length and energy scales, determined by the
breakout opacity, velocity and density, the solution is universal, i.e. depends
only on the density power law index n. The resulting luminosity depends weakly
on the value of n. An approximate analytic solution, based on the self-similar
hydrodynamic solutions and on the steady RMS solutions, is constructed and
shown to agree with the numerical solutions as long as the shock is far from
the surface, \tau>> c/v_{sh}. Approximate analytic expressions, calibrated
based on the exact solutions, are provided, that describe the escaping
luminosity as a function of time. These results can be used to calculate the
bolometric properties of the bursts of radiation produced during supernova (SN)
shock breakouts. For completeness, we also use the exact breakout solutions to
provide an analytic approximation for the maximum surface temperature for fast
(v_{sh}>~0.1) non-thermal breakouts, and show that it is few times smaller than
inferred based on steady-state RMS solutions.
