  Hodograph equations for the n-dimensional Euler equations with the constant
pressure and external force linear in velocity are presented. They provide us
with solutions of the Euler in implicit form and information on existence or
absence of gradient catastrophes. It is shown that in even dimensions the
constructed solutions are periodic in time for particular subclasses of
external forces. Several particular examples in one, two and three dimensions
are considered, including the case of Coriolis external force.
