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.

Hint: Write $$y'=\frac{2+\frac{y}{x}}{-1+\frac{y}{x}}$$ and substitute $$u=\frac{y}{x}$$
