Particular Solutions to One Kind of Second Order Matrix Differential Equation

Based on differential equations theory and matrix theory,and by the method of column comparison and undermined matrix,the particular solution of a kind of three-dimensional second order differential equations with constant coefficients is obtained.And the non-homogeneous terms of differential equations are the form of quadratic polynomial multiplied by exponential function.The special cases are discussed in detail.For example,the particular solution formulas are validated.The research results have provided a foundation for the study of the method of solving on differential equations.