(a) Show that every member of the family of functions y = (4 ln(x) + C)/x , x > 0, is a solution of the differential equation x2y' + xy = 4. (Simplify as much as possible.) y = 4 ln(x) + C x ⇒ y' = 4x · (1/x) − (4 ln(x) +C) x2 LHS = x2y' + xy = x2 · $$ Incorrect: Your answer is incorrect. x2 + x · 4 ln(x) + C x = Correct: Your answer is correct. + 4 ln(x) + C = Correct: Your answer is correct. = RHS, so y is a solution of the differential equation. (b) Illustrate part (a) by graphing several members of the family of solutions on a common screen.