Chapter 6.4, Problem 15E

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

Calculus (MindTap Course List)

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

Slope Field In Exercises 15 and 16, (a) sketch an approximate solution or the differential equation satisfying the given initial condition on the slope field, (b) find the particular solution that satisfies the given initial condition, and (c) use a graphing utility to graph the particular solution. Compare the graph with the sketch in part (a). To print an enlarged copy of the graph, go to MaihGraphs.com. d y d x = e x − y

(a)

To determine

To graph: An approximate solution of the differential equation, dydx=exy, satisfying the initial condition, (0,1) on the slope field.

Explanation

Given:

The differential equation is, dydx=exâˆ’y, the initial condition is, (0,1), and the slope field is shown below,

Graph:

Consider the given differential equation,

dydx=exâˆ’y

Make a table for the slopes at different points as shown below,

 x âˆ’2 âˆ’2 âˆ’1 âˆ’1 0 0 1 1 2 2 y 1 âˆ’1 1 âˆ’1 1 âˆ’1 1

(b)

To determine
The particular solution of the differential equation, dydx=exy, satisfying the initial condition, (0,1) on the slope field.

(c)

To determine

To graph: The particular solution, y=12(ex+ex), using graphing utility and compare the graph with the graph obtained in part (a).

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