Self-consistent stationary equilibrium states of a quasineutral, self-gravitating dusty plasma have been investigated by avoiding the usual "Jeans swindle" assumption. The analysis has been carried out for the Cartesian one-dimensional, cylindrical, as well as spherical symmetric cases. It is shown that allowed equilibria permit steady but inhomogeneous dust flows governed by a nonlinear differential equation, which has a singularity at the dust-acoustic speed. The qualitative nature of the admissible solutions of the latter equation have been discussed. The corresponding results for the case of a self-gravitating neutral fluid have also been pointed out.