Abstract: For any well-posed problem of the equation of wave motion or heat conduction with inhomogeneous boundary conditions in higher ( two or three) dimensions， an auxiliary problem is proposed. Using the solution of the latter， the original problem is transformed to one with homogeneous boundary conditions. This method for solving problems with inhomogeneous boundary conditions is widely applicable and easy to follow. Solutions for two examples are presented.

Key words: equation of wave motion； equation of heat conduction； , inhomogeneous boundary conditions； auxiliary problem