Solve: $\frac{dy}{dx} - \frac{dx}{dy} = \frac{y}{x} - \frac{x}{y}$
What I have done till now: $\left(\frac{dy}{dx}\right)^2 -1= \frac{dy}{dx}\left(\frac{y}{x} - \frac{x}{y}\right)$ $xy\left(\frac{dy}{dx}\right)^2 - xy= \frac{dy}{dx}\left({y^2} - {x^2}\right)$ Now I am stuck.
EDIT: I have been through a course on ODEs (More like a course which added tools to our toolbox to solve ODEs) but it has been a long time since then. Everytime someone helps me with an answer it is an "Oh Yes! I forgot about that" moment. Is there any resource (Succinct PDF preferably) which can help me revise the tools used for solving ODEs? This looked good but I want more examples and methods.