Transcription of Chapter 16 F D IRST IFFERENTIAL -ORDER EQUATIONS
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Chapter 16 F D IRST IFFERENTIAL -ORDER EQUATIONS
Chapter FIRST -ORDER . 16 DIFFERENTIAL EQUATIONS . OVERVIEW In Section we introduced differential EQUATIONS of the form dy>dx = (x), where is given and y is an unknown function of x. When is continuous over some inter- val, we found the general solution y(x) by integration, y = 1 (x) dx. In Section we solved separable differential EQUATIONS . Such EQUATIONS arise when investigating exponen- tial growth or decay, for example. In this Chapter we study some other types of first -ORDER differential EQUATIONS . They involve only first derivatives of the unknown function. Solutions, Slope Fields, and Picard's Theorem We begin this section by defining general differential EQUATIONS involving first derivatives.
OVERVIEW In Section 4.7 we introduced differential equations of the form , where is given and y is an unknown function of . When is continuous over some inter-val, we found the general solution by integration, . In Section 7.5 we solved separable differential equations.
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