Solutions of systems of linear differential equations with constant coefficients in education of automation

摘要

Systems of linear differential equations with constant coefficients occur in the area of operations research very frequently. These arise, for example, as mathematical models of dynamical systems. One can solve linear systems using the method of variation of parameters or using Laplace transform. Sometimes, for the given system, both the methods can be used, while in other cases we can solve it only by one of the methods. In particular, if the system is an initial value problem with discontinuous forcing terms we (frequently) have to solve it using Laplace transform. On the other hand, if there are boundary conditions of special types, it is not possible to use Laplace transform. In this contribution we show how to solve it in both cases and we also show that the student of automation have to know both the ways of solution.