(a) The solution of the differential equation

{2xy/(x² + y²)² [1 + (y² – x²)/(x² + y²)²]dy = 0

is a family of curves that can be interpreted as streamlines of a fluid flow around a circular object whose boundary is described by the equation x² + y² = 1. Solve this DE and note the solution f (x, y) = c for c = 0.

(b) Use a CAS to plot the streamlines for c = 0, ± 0.2, ±0.4, ±0.6, and ±0.8 in three different ways. First, use the contourplot of a CAS. Second, solve for x in terms of the variable y. Plot the resulting two functions of y for the given values of c, and then combine the graphs. Third, use the CAS to solve a cubic equation for y in terms of x.