Integrals of systems of linear differential equations with constant coefficients. (Q2901589)

This paper addresses the issue of constructing the complete family of integrals for a linear system of ordinary differential equations. It is assumed that the system under consideration has constant coefficients. To integrate such a system, the authors consider its matrix in the Jordan canonical form. A detailed study of integrals is carried out depending on the order of the Jordan blocks. For the case of complex eigenvalues, explicit expressions of the integrals are given in real variables.