Determine a region of the xy-plane for which the given differential equation would have a unique solution whose graph passes through a point (x₀, y₀) in the

1. dy/dx = y^2/3

2. dy/dx = √xy

3. x dy/dx = y

4. dy/dx –y = x

5. (4 – y²)y' = x²

6. (1 + y³)y' = x²

7. (x² + y²)y' = y²

8. (y - x)y' = y + x