三阶微分方程组特解的按列比较法

Column Comparison Method for the Special Solution of Three Order Differential Equations

基于矩阵微分方程理论,采用按列比较法和待定矩阵法,给出了非齐次项为三次多项式与指数函数乘积的一类二维三阶常系数微分方程组的特解公式,利用算例验证了特解公式的正确性.

Based on the theory of matrix differential equation and by using column comparison method and undetermined matrix method, a particular solution of a kind of systems of two-dimensional third order differential equations with constant coefficients are given. It is thus proved that the non-homogeneous terms of differential equations are the form of the cubic polynomial multiplied by exponential function. For example, the particular solution formulas are validated.