复杂二阶常系数非齐次线性微分方程的特解问题

Special Solutions of Complex Second Order Nonhomogeneous Linear Differential Equations with Constant Coefficients

本文根据已有的微分方程基础知识,讨论了复杂二阶常系数非齐次微分方程,形如y''+py'+qy=e^(λx)[(α_0+α_1x)cosωx+(b_0+b_1x)sinωx]的特解的一般公式。通过应用公式,避免了求解三因式相乘的二阶导数的繁杂工作,大大化简了特解的求解过程,从而删繁就简。

In this paper, we discuss the complex second order nonhomogeneous differential equations with constant coefficients according to the basic knowledge of differential equations, general formula of special solution such as y''+py'+qy=e^(λx)[(α_0+α_1x)cosωx+(b_0+b_1x)sinωx].By applying the formula, the complicated work of solving the second derivative of the multiplication of the three factors is avoided, and the process of solving the special solution is greatly simplified.