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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. As the course unfolds, you will see that there is moreto the study of DIFFERENTIAL EQUATIONS than just mastering methods that someone hasdevised to solve first things first.

Course in Differential Equations with Modeling Applications, Ninth Edition. In that text the word equation and the abbreviation DE refer only to ODEs. Partial differential equations or PDEs are considered in the expanded volume Differential Equations with Boundary-Value Problems, Seventh Edition.

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