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In a multidimensional infinite layer bounded by two hyperplanes, theinhomogeneous Helmholtz equation with a polynomial right-hand side isconsidered. It is shown that the Dirichlet and Dirichlet-Neumann boundary-valueproblems with polynomials in the right-hand sides of the boundary conditionshave a solution that is a quasipolynomial that contains, in addition to thepower functions, also hyperbolic or trigonometric functions. This solution isunique in the class of slow growth functions if the parameter of the equationis not an eigenvalue. An algorithm for constructing this solution is given andexamples are considered.

Exact solutions of the boundary-value problems for the Helmholtz  equation in a layer with polynomials in the right-hand sides of the equation  and of the boundary conditions