Problem 6: [15 pts] Consider the differential equation dy + xy = y2, whose direction field is shown below. dx I. [3 pts] Use the direction field to explain if there is a real number r so y = e" is a solution to dy + xy = y2. II. [4 pts] Substitute y = e" into the differential equation dy + ry = y?, then use the result explain whether there is any real number r so y = ett is a solution. dx III. [8 pts] Suppose that y = f(x) is a solution to the initial value problem em dy + xy = y?, y(0) = 2. Calculate the second degree Taylor polynomial centered at . = 0