  An inhomogeneous Tricomi equation is considered in a strip with a polynomial
right-hand side. It is shown that the Dirichlet boundary value problem with
polynomial boundary conditions has a polynomial solution. An algorithm for
constructing this polynomial solution is given and examples are considered. If
the strip lies in the ellipticity region of the equation, then this solution is
unique in the class of functions of polynomial growth. If the strip lies in a
mixed region, then the solution of the Dirichlet problem is not unique in the
class of functions of polynomial growth, but it is unique in the class of
polynomials.
