Assume that the implicit function $\displaystyle e^{xy} = y$ determines y as a differentiable function of x in some interval. Without attempting to solve the equation for y(x), show that y(x) satisfies the differential equation $\displaystyle (1-xy)y' - y^2 = 0$.

I started by finding the derivative of y.

$\displaystyle y' = y'e^x \Rightarrow$

$\displaystyle e^{xy} = 1$

I am unsure of what to do next to answer the question.

EDIT: Looking at this problem more, I realized that I forgot to use the multiplication rule when finding the derivative of $\displaystyle xy$