Linear system of first-order differential equations

Abstract

In this seminar we will give a general solution of n-dimensional first-order system of ordinary differential equations. Such a system arises naturally in problems involving several dependent variables each of which is a function of a single independent variable. We will denote the independent variable by t, and x1, x2, …, xn represent dependent variables which are functions of t. The chapter one we will represent some of important definitions and theorems that we will need them in our subject. Then in chapter two, we will study the methods for contracting the general solution of homogeneous and non-homogeneous linear first-order system differential equations.