中文摘要：

基于微分方程组理论和矩阵理论，采用待定矩阵方法和按列比较方法，给出了非齐次项为二次多项式与指数函数乘积的一类三维二阶常系数线性微分方程组的特解公式，对二种特殊情况进行了讨论，并通过算例验证了微分方程组特解公式的正确性。为高阶微分方程组的解法研究提供了一条有效的途径。

英文摘要：

Based on differential equations theory and matrix theory, and by the method of undermined matrix and column comparison, the paper is devoted to provide a particular solution of finding a kind of systems of three-dimensional second order differential equations with constant coefficients. And the non-homogeneous terms of differential equations are the form of quadratic polynomial multiplied by exponential function. Two special caseses are discussed in detail. For example, the particular solution formulas are validated. The results presented in the paper are generalization of previous works done by the authors of the paper, thus griving a foundation for the study of the method of solve on differential equations.