   Chapter 6.1, Problem 55E

Chapter
Section
Textbook Problem

Slope Field In Exercises 53–56, a differential equation and its slope field are given. Complete the table by determining the slopes (if possible) in the slope field at the given points. x - 4 - 2 0 2 4 8 y 2 0 4 4 6 8 d y d x d y d x = x   cos   π y 8 To determine

To Calculate: The slopes (if possible) in the slope field at the points provided.

Explanation

Given:

The differential equation: dydx=xcos(πy8)

Formula Used:

dydx=xcos(πy8)

Calculation:

It is given that the differential equation is:

dydx=xcos(πy8)

At the point (4,2) the slope is: dydx=(4)cos(π.28)=4cos(π4)=4.12=22

At the point (2,0) the slope is: dydx=(2)cos(π.08)=2cos(0)=2.1=2

At the point (0,4) the slope is: dydx=0.cos(π.48)=0.cos(π2)=0

At the point (2,4) the slope is: dydx=2

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