常系数线性微分方程特解系数的迭代公式

Particular solution's iterative formula of linear differential equation with constant coefficients

在现行的《高等数学》教材中,求解微分方程 y″+py′+qy=q^(λx)P_m(λ)[acosωx+bsinωx)的特解,都采用待定系数法。 本文给出了待定系数的m+1个或2(m+1)个联立方程组的显式表示,省略繁琐的计算,并且由此给出了待定系数的迭代公式。

In present textbooks 'High Mathematics', the undetermined coefficient method is used to getting the particular solutions of linear differential equation with constant coefficients.This method is tedious in calculation. Now, the explicit expression of the system of equation included m + 1 or 2(m+1) equations and the iterative formula of undetermined coefficients are given,and the complex calculating processes are simplified.