一道求微分方程特解习题的推广

A Generalization of a Special Solution of Differential Equations

讨论了二阶常系数线性非齐次微分方程当非齐次项f(x)=P_m(x)e^(λx)中Pm(x)为二次多项式时特解的简便求法。根据λ是否是特征根的情形,利用待定系数法,给出了具体的求解公式,简化了求特解的计算过程和难度.

The paper presents a simple method for solving the special solution.to the two order constant-coefficient linear differential equation when nonhomogeneous term,if is quadratic polynomial.According to whether is a characteristic root or not,using undetermined coefficient method,the solution formula is given,which simplified the calculation process and difficulty of solving special solution.