   Chapter 6.3, Problem 37E

Chapter
Section
Textbook Problem

Slope Field In Exercises 35-38, (a) write a differential equation for the statement, (b) match the differential equation with a possible slope field, and (c) verify your result by using a graphing utility to graph a slope field for the differential equation. [The slope fields are labeled (i), (ii), (iii), and (iv).] The rate of change of y with respect to x is proportional to the product of y and the difference between y and 4.

(a)

To determine

To Calculate: The differential equation of the statement, “The rate of change of y with respect to x is proportional to the product y and the difference between y and 4”.

Explanation

Given:

The statement, “The rate of change of y with respect to x is proportional to the product y and the difference between y and 4”.

Formula used:

The rate of change of y with respect to x is given by dydx.

Calculation:

Let us consider the given differential is as follows:

dydxα

(b)

To determine
The correct match of the differential equation dydx=ky(y4).

(c)

To determine

To prove: The result by using graphing utility to graph a slope field for the differential equation dydx=yk(y4) .

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