Variable Change In A Differential Equation If I have the following differential equation:
$\dfrac{dy}{dx} = \dfrac{y}{x} - (\dfrac{y}{x})^2$ 
And if I make the variable change: $\dfrac{y}{x} \rightarrow z$
I know have $\dfrac{dy}{dx} = z-z^2$
What is $\dfrac{dx}{dy}$ after the variablechange?

If you make $y=x z$, $y'=x z'+z$ and the equation becomes $$x z'+z=z-z^2$$ that is to say $$x z'=-z^2$$which is separable.
