For a first-order DE dy/dx = f (x, y) a curve in the plane defined by f (x, y) = 0 is ca...

For a first-order DE dy/dx = f (x, y) a curve in the plane defined by f (x, y) = 0 is called a nullcline of the equation, since a lineal element at a point on the curve has zero slope. Use computer software to obtain a direction field over a rectangular grid of points for dy/dx = x² - 2y, and then superimpose the graph of the nullcline over the direction field. Discuss the behavior of solution curves in regions of the plane defined by and by Sketch some approximate solution curves. Try to generalize your observations.