Determining a Particular Solution for the Systems of Linear Differential Equations with Constant Coefficients

As with the n-th order linear differential equations with constant coefficients, the problem to be solved is related to determining a particular solution, and then, using the general solution of the attached homogeneous system of linear differential equations with constant coefficients, to write the general solution of the initially given system. For homogeneous systems of linear differential equations with constant coefficients, the determination of the general solution is the method of eliminating or reducing which make the system a linear differential equation of the same order as that of the system, and its methods of solving it applies or the method of own values and vectors. If the system is non-homogeneous, then we also have to determine a particular solution that can be done in the same way as in the case of n-th order differential equations with constant coefficients, if the method of reduction or elimination was used, or the method of variation of constants, regardless of the method used to determine the general solution of the attached homogenous system of linear differential equations with constant coefficients. Whichever method is used, determining a particular solution for a system of linear differential equations with constant coefficients is difficult, in this study being proposed a method similar to that of n-th order linear differential equations with constant coefficients.