Abstract: One of the un-determined functions methods for solving the deterministic problems with non-homogeneous boundary conditions by using the method of variable separation has been presented, which can homogenize boundary conditions and differential equation simultaneously. Also the deterministic problems of three typical kinds of mathematical physical equations with the first, the second or the third type of the non-homogeneous boundary conditions are discussed, respectively. The specific conclusions and the solving model are presented.

Key words: method of separation of variables, non-homogeneous boundary conditions, wave equation, transport equation, Laplace equation, three kinds of boundary conditions, second-order linear ordinary differential equation