  In this article we report a novel analytic solution for a cosmological model
with a matter content described by a one component dissipative fluid, in the
framework of the causal Israel-Stewart theory. Some physically well motivated
analytical relations for the bulk viscous coefficient, the relaxation time and
a bariotropic equation of state are postulated. We study within the parameter
space, which label the solution, a suited region compatible with an accelerated
expansion of the universe for late times, as well as stability properties of
the solution at the critical parameter values $ \gamma = 1$ and for $ s = 1/2
$. We study as well the consequences that arise from the positiveness of the
entropy production along the time evolution. In general, the accelerated
expansion at late times is only possible when $\epsilon\geq 1/18$, which
implies a very large non-adiabatic contribution the speed of sound.
