   Chapter 6, Problem 9RE

Chapter
Section
Textbook Problem

Slope Field In Exercises 9 and 10, 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 = 2 x − y To determine
The values in the table by determining the slope in the slope field for dydx=2xy.

Explanation

Given:

The function dydx=2xy

The graph:

Explanation:

Let f(x,y)=2xy.

The value of f at the point (4,2) is:

f((4),2)=2(4)2=82=10

So, the value of dydx at the point (4,2) is 10.

The value of f at the point (2,0) is:

f((2),0)=2(2)(0)=4

So, the value of dydx at the point (2,0) is 4.

The value of f at the point (0,4) is:

f(0,4)=2(0)(4)=4

So, the value of dydx at the point (0,4) is 4

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