1 - INTRODUCTION

Abstract

This chapter discusses the initial value problem for differential equations and illustrates several examples of initial value problems. It discusses first-order ordinary differential equations, presents the systems of first order ordinary differential equations, provides a classification of the systems of first-order differential equations, the discusses nth order ordinary differential equations, and presents complex valued ordinary differential equations. The chapter explains the autonomous system of first -order ordinary differential equations, the periodic system of first-order differential equations, the linear homogeneous system of ordinary differential equations, the linear periodic system of ordinary differential equations, the linear nonhomogeneous system of ordinary differential equations, and the linear, autonomous, homogeneous system of ordinary differential equation. Mechanical translation systems obey Newton's second law of motion, which states that the sum of the applied forces (to a point mass) should equal the sum of the reactive forces.