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Ordinary Differential Equations: A Systems Approach

Ordinary Differential Equations: A Systems ApproachBruce P. ConradNovember 24, 20101c 2010 Bruce P. Conrad2 Chapter 1 First-Order Equations34 CHAPTER 1. FIRST-ORDER IntroductionA Differential equation is a relation involving an unknown function andsome of its derivatives. For example,dydt=y+etis a Differential equation that asks for a function,y=f(t), whose derivativeis equal to the function pluset. By differentiating, you can verify that afunction such asy=tetmeets this equations are a source of fascinating mathematical prob-lems, and they have numerous mathematical model is a mathematical construction, such as a differ-ential equation, that simulates a natural or engineering phenomenon.

4 CHAPTER 1. FIRST-ORDER EQUATIONS 1.1 Introduction Adifferential equationis a relation involving an unknown function and some of its derivatives. For example, dy dt = y +et is a differential equation that asks for a function, y = f(t), whose derivative is equal to the function plus et. By differentiating, you can verify that a

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