Sketch the direction field for the following DEs for -2 <= x <= 2 and -2 <= y <= 2. (a) y^'=x-y (b) y^'=x y

To sketch the direction field for the given differential equations, you would typically use a software tool like MATLAB or Python's Matplotlib. However, I can guide you through the steps you would take to do this.

1. Define the range of x and y. In this case, it's -2 <= x <= 2 and -2 <= y <= 2.

2. For each point in this grid, calculate the slope using the given differential equation.

(a) For y'=x-y, the slope at any point (x, y) on the plane would be calculated by subtracting the y-coordinate from the x-coordinate.

(b) For y'=xy, the slope at any point (x, y) on the plane would be calculated by multiplying the x-coordinate and the y-coordinate.

3. Draw a small line segment at each point in the direction of the slope. The length of the line segment typically does not matter and does not affect the final sketch of the direction field.

4. Repeat this process for each point in the grid. The resulting plot of line segments will give you the direction field for the differential equation.

Remember, the direction field gives a visual representation of the solutions to the differential equation. Each line segment represents the slope or direction of the solution curve at that point.