Use computer software to obtain a direction ­field for the given differential equation. By hand, sketch an approximate solution curve passing through each of the given points.

1. y' = x

(a) y(0) = 0

(b) (-2)

2. y' = x + y

(a) y(-2) = 2

(b) y(1) -3

3. y dy/dx = -x

(a) y(1) = 1

(b) y(0) = 4

4. dy/dx = 1/y

(a) y(0) = 1

(b) y(-2) = -1

5. dy/dx = 0.2x² + y

(a) y(0) = ½

(b) y(2) = -2

6. dy/dx = xe^x

(a) y(0) = -2

(b) y(1) = 2.5

7. y' = y – cos π/2 x

(a) y(2) = 2

(b) y(-1) = 0

8. dy/dx = 1 – y/x

(a) y(-1/2) = 2

(b) y(3/2) = 0