TITLE: Solve this differential equation $\Biggr(\frac{dy}{dx} -1\Bigg)\Bigg(y-x\frac{dy}{dx}\Bigg)=\frac{dy}{dx}$
QUESTION [5 upvotes]: Solve this differential equation:
  $$\Biggr(\frac{dy}{dx} -1\Bigg)\Bigg(y-x\frac{dy}{dx}\Bigg)=\frac{dy}{dx}$$

How to solve this?

REPLY [2 votes]: Since nmasanta already posted the answer I don't edit my calculus. 
I only add the singular solution $y=x+1\pm 2\sqrt{x}$ and a graph of the complete solutions of the ODE :