  An explicit solution for a general two-type birth-death branching process
with one way mutation is presented. This continuous time process mimics the
evolution of resistance to treatment, or the onset of an extra driver mutation
during tumor progression. We obtain the exact generating function of the
process at arbitrary times, and derive various large time scaling limits. In
the simultaneous small mutation rate and large time scaling limit, the
distribution of the mutant cells develops some atypical properties, including a
power law tail and diverging average.
