Question

Consider curve -x^2 + 2xy + 2y^2 = 3
Show that (x +2y)y' - x + y =0 ?

Answer 1

derive implcitly from both sides :
-x^2 + 2xy + 2y^2 = 3
-2x + 2y + 2x y' + 4y y' = 0
divide by 2 from both sides, will giving us
-x + y + x y' + 2y y' = 0
y' (x+2y) - x + y = 0

QED