Particular Solutions to a Kind of Matrix Ordinary Differential Equation

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.