How to find the singular solution of $y'=\frac{2x+y}{y-x}$ $y'$ and $y$ occur linearly in the ODE
$$y'=\frac{2x+y}{y-x}.$$
yet it is a first order non-linear ODE. I can find a family  solutions of this homogeneous ODE by using $y=vx \implies \frac{dy}{dx}= v+x \frac{dv}{dx}$. I want to know if there is(are) singular solution(s) of this equation.

$$ y'=\frac{x(2+\frac{y}{x})}{x(\frac{y}{x}-1)} $$ 
then you can make a replacement $$  t=\frac{y}{x} \Rightarrow \frac{dy}{dx}=\frac{dt}{dx}x+t \Rightarrow \frac{dt}{dx}x+t=\frac{2+t}{t-1}     $$
It remains only to divide the variables and take the integral :)
