For a first-order DE dy/dx =f (x, y) a curve in the plane defined…

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 slopes. Use computer software to obtain a direction field over a rectangular grid of points for dy/dx =x^2 – 2y, and then superimpose the graph of the nullcline y= 1/2x^2 direction field. Discuss the behavior of solution curves in regions of the plane defined by y < 1 /2 x^2 and by y > 1/2 x^2. Sketch some approximate solution curves. Try to generalize your observations