Chapter 6.1, Problem 46E

To determine

To choose : The correct graph.

Answer to Problem 46E

The correct graph is: Graph $(a)$

  

Explanation of Solution

Given information:

The differential equation is: $\frac{dy}{dx}=xy$

Calculation:

For $\frac{dy}{dx}=xy$ ,

  $\frac{dy}{dx}=0$

Whenever $x=0$ or

  $y=0$

The graph must then have horizontal line segments at all points with an $x$ -coordinate of 0 and at all points with a $y$ -coordinate of 0.

The correct slope field is then $(a)$ .

Start at $(0,2)$ to begin drawing the graph of the specific answer $(0,2)$ . Sketch a section of the curve with a roughly equal slope using the line segment at that location.

Sketch another section of the curve with the same slope as the line segment close to  sketch at $x=1$ Up to the point where the sketch is completely filled in, keep doing this on both sides of $x=0$ . The drawing is displayed below.

  

Therefore the required graph $(a)$ is match the given differential equation with the appropriate slope field.