Integrating factors 1. a) verify that p(x, y) = (x+y)2 is an integrating factor for -y^2 dx + x² dy = 0 on any open rectangle that does not intersect the line y = x. b) find a family of solutions to the previous equation of the form f(x, y) = c, where c is an arbitrary constant. c) verify that y = x is a solution of the original differential equation even though it cannot be obtained from f(x, y) = c with the function f obtained in b) above.