Solve $y'' - y' = yy'$ and find three Other Distinct Solutions Been stuck on this for a while. I need to solve the following differential equation by finding the constant solution y = c and three other distinct solutions.
$$y'' - y' = yy'$$
If someone could give me a complete step by step explanation, it would be greatly appreciated as I want to fully understand it.

I'll assume the independent variable is $x$, you can make the necessary changes if it's $t$ or anything else.
Let $z=y'$.  Then
$$y''=\frac{dz}{dx}=\frac{dz}{dy}\frac{dy}{dx}=z\frac{dz}{dy}$$
and substituting into the DE gives
$$z\frac{dz}{dy}-z=yz\ .$$
See if you can take it from here.
