  In this paper, we discuss a general method to obtain exact cosmological
solutions in modified gravity, to demonstrate the method it is employed to
obtain exact cosmological solutions in $f(R,\phi)$ gravity. Here, we show that,
given a particular evolution of the Universe, we could obtain different models
of gravity that give that evolution, using the same construction. Further, we
obtain an exact inflationary solution for Starobinsky action with a negligible
cosmological constant. This analysis helps us to have a better understanding of
Starobinsky inflation. With our analysis we could refine the parameter values
and predictions of Starobinsky inflation. Also, we make an observation that
there exist a no-go theorem for a bounce from Starobinsky action in the absence
of scalar fields or a cosmological constant.
