About the approximate solution of a boundary value problem for an inhomogeneous biharmonic equation

The boundary task for an inhomogeneous biharmonic equation, describing the static deflection of the fixed along the edges rectangular plate under the concentrated force action enclosed to a point with coordinates $(\widetilde x,\widetilde y)$ is considered. Special solution of a differential equation is determined as specially selected expansion in some base functions, each of them exactly complies with the given boundary conditions. The possibility of series Green's function decomposition of examined boundary value problem in it's eigenfunctions is determined the works of D. Hilbert and R, Courant. It leads to plain approximate analytical expressions for solutions and eigenvalues of the boundary task. Errors of the approach are estimated.