一类二阶微分方程组的通解

General Solutions to One Kind of Systems of Second-order Ordinary Differential Equation

采用降阶和特征根(欧拉)方法,给出一类三维二阶常系数微分方程组的通解公式,并通过算例与拉氏变换法进行比较,说明利用该通解公式求解高阶微分方程组比采用其他方法求解更简捷,且具有通用、严谨、清晰和实用等优点.

By reducing order and using Euler＇s eigenvalue method, the general solution formula to one kind of three-dimensional second-order ordinary differential equation groups with constant coefficients is obtained. The methods used in this paper are compared with the method using Laplacian transform with examples. It is illustrated that using general solution formula to solve the high-order differential equation groups is more concise than other methods in accuracy, clarity and practicability.