I am stuck on b, c, and d. Please show me detailed steps.

(2,2) (0,2) II (0,0) (2,0) Exercise 1 Let of = (2xy - x2y) dx + (x2 - x2y) dy (a) Show that of is an inexact differential. (b) Consider two path in the xy-plane from (0, 0) to (2,2): Path I: (0,0) - (2,0) at constant y then from (2, 0) - (2,2) at constant x. Path II: (0,0) - (0,2) at constant x then from (0,2) - (2,2) at constant y. Show the line integral along paths I and II yield different values demonstrating again the differential to be inexact. (c) An integrating factor, $(x, y), is a function which multiplies an inexact differential to make it exact. dg (x, y) = $(x, y ) of If o(x,y) = xym. Determine the form of the integration factor (what are m and n?). Hint: When does ay($ (2xy - x2y) ) = ax($ (x2 -x2y))? (d) Now with the integrating factor determined in (c). Repeat the calculations in (a) and verify dg is now an exact differential