Chapter 7.1, Problem 74E

To determine

To find the correct differential equation from the given choices which possess the given slope field.

Answer to Problem 74E

The differential equation $\frac{dy}{dx}=y-\left|x\right|$ possess the slope field,

  

Explanation of Solution

Given information :

The slope field,

  

The choices of differential equations are,

1. $\frac{dy}{dx}=y-\left|x\right|$
2. $\frac{dy}{dx}=\left|y\right|-x$
3. $\frac{dy}{dx}=\left|y-x\right|$
4. $\frac{dy}{dx}=\left|y+x\right|$
5. $\frac{dy}{dx}=\left|y\right|-\left|x\right|$

Calculation:

Clearly the given slope field contain both positive and negative slopes.

Here, the option C $\frac{dy}{dx}=\left|y-x\right|$ and D $\frac{dy}{dx}=\left|y+x\right|$ will only result in positive slope since they are absolute values.

For the option B $\frac{dy}{dx}=\left|y\right|-x$ it will result in positive slopes in third quadrant of its slope field. But in the given slope field it contains all negative slopes in the third quadrant.

Hence, option B should be eliminated.

Considering the option E $\frac{dy}{dx}=\left|y\right|-\left|x\right|$ when $x=0$ the slope the slope field has negative slopes when $y<0$ .

Hence option B can also be eliminated.

Therefore, the correct option is, option A $\frac{dy}{dx}=y-\left|x\right|$ .

Thus, the slope field of the differential equation $\frac{dy}{dx}=y-\left|x\right|$ is,