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Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

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BuyFindarrow_forward

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

Slope Field In Exercises 61–64, (a) sketch the slope field for the differential equation, (b) use the

slope field to sketch the solution that passes through the given point, and (c) discuss the graph of

the solution as and Use a graphing utility to verify your results. To print a blank graph, go to

MathGraphs.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=y4x 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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