线性非齐次方程待定函数法及相关定理证明

Theorem of method of undetermined function for linear nonhomogeneous and its proof

把数理方程混合问题的方程和边界条件视为一个整体,给出了齐次方程加齐次边界条件的形式通解的概念并证明了相关定理,还证明了非齐次方程加非齐次边界条件的形式通解的结构定理,总结了待定函数法解题步骤及一般形式,提供了求解线性非齐次方程混合问题的简便解法。

In this paper, regarding the boundary condition of the mixed problem of equation of mathematical physics as a unity, we present the concept of formal general solution of homogeneous equation with homogeneous boundary condition and the proof of relevant theorem. Furthermore, we prove the structure theorem of general solution of nonhomogeneous equation with nonhomogenous boundary condition. Finally, we list the steps of method of undetermined function and its applicable range, This paper provides a simple method for solving the mixed problem of linear nonhomogeneous equation.