The particular solutions to one kind of second order matrix ordinary differential equation

In the light of differential equation and matrix theory,this paper provides a particular solution to the three-dimensional second order differential equations with constant coefficients by using the method of undermined matrix and column comparion.It is proved that the non-homogeneous terms of differential equations are the form of tregonometric functions multiplied by exponential function and the particular solution formulas are validated,which provides an effective method for the study of the solution to the differential equation of higher order.