  In this paper, I present an analytic solution to the equation of motion of
the inflaton field in a model of rapid roll inflation with a quartic potential
by assuming that the Hubble parameter is a constant during inflation. The
result is obtained by using Jacobi elliptic functions. The spectral index $n_s$
and the running spectral index $n_s^\prime$ is obtained without using rapid
roll or extended slow roll approximations. The cosmological consequences of the
model is discussed.
