Chapter 7.1, Problem 25E

To determine

To match the differential equation with the graph of a family of functions

Answer to Problem 25E

Option $\left(b\right)$ represents the graph of the differential equation $\frac{dy}{dx}={\left(\sin x\right)}^2$ .

Explanation of Solution

Given information:

The differential equation given is $\frac{dy}{dx}={\left(\sin x\right)}^2$

The graphs given are

  

Calculation:

The differential equation given is $\frac{dy}{dx}={\left(\sin x\right)}^2$ .The slope at any point $\left(0,y\right)$ is ${\left(\sin 0\right)}^2=0$ therefore along y-axis there are tiny segments with slope $0$ (lines parallel to x-axis).The slope at any points $\left(\frac{\pi }{2},y\right)$ and $\left(-\frac{\pi }{2},y\right)$ will be $1$ and $-1$ .

. As the slope ${\left(\sin x\right)}^2$ contains even power therefore the graph will not be much flatten it will be more slanted.

Hence option $\left(b\right)$ represents the graph of the differential equation $\frac{dy}{dx}={\left(\sin x\right)}^2$ .