  We prove that the field equations of the Starobinsky model for inflation in a
Friedmann-Lema\^{\i}tre-Robertson-Walker constitute an integrable system as the
field equations pass the singularity test. The analytical solution in terms of
a Painlev\'{e} Series for the Starobinsky model is presented for the case of
zero and nonzero spatial curvature. In both cases the leading-order term
describes the radiation era provided by the corresponding higher-order theory.
