What Type of Differential Equation is $ \frac{dy}{dx} = \frac{1}{x(x-y)} $

Question

What type of differential equation is this?

$$
\frac{dy}{dx} = \frac{1}{x(x-y)}
$$

I am stuck on this problem and can't seem to find any solution for it. Is it separable, homogeneous, exact, linear, or Bernoulli? Can anyone help?

Answer 1

Hint

Switching variables makes to problem looking easier $$\frac{dy}{dx} = \frac{1}{x(x-y)}\implies \frac{dx}{dy}=x(x-y)$$So, asssuming $x\neq 0$ $$\frac 1 x \frac{dx}{dy}-x=-y$$