Question

Determine d^2y/dx^2 if 2xy-y^2=3

Answer 1

2y + 2xy' - 2yy' = 0

y'(2x-2y) = -2y
y' = y/(y-x)

y" = (y'(y-x) - y(y'-1))/(y-x)^2
= (-xy'+y)/(y-x)^2
= (-x(y/(y-x)+y)/(y-x)^2
= ((-xy+y(y-x))/(y-x)^3
= (y^2-2xy)/(y-x)^3