Ordinary Differential Equations and Linear Systems of Ordinary Differential Equations

Abstract

In this chapter, we provide a method for solving systems of linear ordinary differential equations by using techniques associated with the calculation of eigenvalues, eigenvectors and generalized eigenvectors of matrices. We learn in calculus how to solve differential equations and the system of differential equations. Here, we firstly show how to represent a system of differential equations in a matrix formulation. Then, using the Jordan canonical form and, whenever possible, the diagonal canonical form of matrices, we will describe a process aimed at solving systems of linear differential equations in a very efficient way.