   Chapter 6.1, Problem 63E

Chapter
Section
Textbook Problem

Slope Field In Exercises 61–64, (a) sketch the slope field for the differential equation, (b) use theslope field to sketch the solution that passes through the given point, and (c) discuss the graph ofthe solution as and Use a graphing utility to verify your results. To print a blank graph, go toMathGraphs.com. y ′ = y − 4 x , ( 2 , 2 )

a)

To determine

To Graph: The slope field for the given differential equation.

Explanation

Given: y=y4x, (2,2)

Graph:

We start by creating a table showing the slopes at several points.

The table shown below is a smallsample. The slopes at many other points should be calculated to get a representative slope field.

 x -2 -2 -1 -1 0 0 1 1 2 2 y -1 1 -1 1 -1 1 -1 1 -1 1 y′=y−4x 7 9 3 5 -1 1 -5 -3 -9 -7

Now, we draw line segments at the points with their respective slopes as shown below

b)

To determine

To Graph: The slope field to sketch the solution that passes through the given point.

c)

To determine
The graph of the solution as x and x.

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