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.

b

step-by-step explanation:

a difference is the result of subtraction. while each of these expressions has subtraction in it, a difference will be the result when subtraction is the last operation applied in the order of operations for the expression. this means subtraction must be outside of the parenthesis. only b has this.

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)

ratio is 2 : 9

the answer is three

13.5 : 3