Transcription of 1 INTRODUCTION TO DIFFERENTIAL EQUATIONS
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1 INTRODUCTION TO DIFFERENTIAL EQUATIONS
11 INTRODUCTION TO and EQUATIONS as Mathematical ModelsCHAPTER 1 IN REVIEWThe words differentialandequationscertainly suggest solving some kind ofequation that contains derivatives y ,y , .. Analogous to a course in algebra andtrigonometry, in which a good amount of time is spent solving EQUATIONS such asx2 5x 4 0 for the unknown number x, in this course oneof our tasks will beto solve DIFFERENTIAL EQUATIONS such as y 2y y 0 for an unknown functiony (x).The preceding paragraph tells something, but not the complete story, about thecourse you are about to begin.
highest derivative y(n) in terms of the remaining n 1 variables. The differential equation, (5) where f is a real-valued continuous function, is referred to as the normal form of (4). Thus when it suits our purposes, we shall use the normal forms to represent general first- and second-order ordinary differential equations.
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