The general method to solve a nonhomogeneous system ODEs with constant coefficients is the method of variation of the constants developed by Lagrange. Sometimes this method leads to integrals that cannot be solved exactly. The techniques we propose to approximate such a system allows to find the approximate solution using eigenvalues and eigenvectors . The results are closer to the exact solution than the results after the integration by series (using MAPLE or calculated by hand). Some examples are given, to compare with these from .