  Recent observational indications of an accelerating universe enhance the
interest in studying models with a cosmological constant. We investigate
cosmological expansion (FRW metric) with $\Lambda>0$ for a general linear
equation of state $p=w\rho$, $w>-1$, so that the interplay between cosmological
vacuum and quintessence is allowed, as well.
  Four closed-form solutions (flat universe with any $w$, and $w=1/3$, $-1/3,
-2/3$) are given, in a proper compact representation. Various estimates of the
expansion are presented in a general case when no closed-form solutions are
available. For the open universe a simple relation between solutions with
different parameters is established: it turns out that a solution with some $w$
and (properly scaled) $\Lambda$ is expressed algebraically via another solution
with special different values of these parameters.
  The expansion becomes exponential at large times, and the amplitude at the
exponent depends on the parameters. We study this dependence in detail,
deriving various representations for the amplitude in terms of integrals and
series. The closed-form solutions serve as benchmarks, and the solution
transformation property noted above serves as a useful tool. Among the results
obtained, one is that for the open universe with relatively small cosmological
constant the amplitude is independent of the equation of state. Also, estimates
of the cosmic age through the observable ratio $\Omega_\Lambda/\Omega_M$ and
parameter $w$ are given; when inverted, they provide an estimate of $w$, i. e.,
the state equation, through the known $\Omega_\Lambda/\Omega_M$ and age of the
universe.
