ABSTRACT
This chapter focuses on systems of linear first order differential equations in normal form when the number of dependent variables is the same as the number of equations. It presents general properties of linear vector differential equations with variable and constant coefficients. The chapter discusses solutions of the initial value problems for nonhomogeneous systems using the variation of parameters, method of undetermined coefficients, and the Laplace transformation. It provides the technique applicable to nonhomogeneous constant coefficient differential equations when the forcing functions are of a special form. The main idea of the method of undetermined coefficients is essentially the same as for a single linear differential equation when the author makes an intelligent guess about the general form of a particular solution. The chapter describes the properties of the solutions for systems of linear nonhomogeneous differential equations with variable coefficients in the normal form.
