  An exact solution of a forced Burgers' equation representing the dynamics of
a "dust fluid" in a one-dimensional flow is presented. The test case considered
starts with a steady (time independent) two-fluid flow in one dimension, where
the two fluid components represent gas and dust. It is then assumed that a
shock wave travels through the gas at a constant speed and without radiative
energy losses and diffusion. Then, adopting a constant stopping time for the
dust particles in the dust fluid (mono-dispersed grain sizes), the equation of
motion for the dust fluid can be transformed into a simple ordinary
differential equation, which is satisfied by the Wright omega function.
Implications for the formation of detached shells around carbon stars are
briefly discussed.
