I am to solve the following differential equation using separation of variables $$f'(x)+2x[f^2(x)-f(x)]=0$$ So far my approach was: $$\frac{df(x)}{dx}+2x[f^2(x)-f(x)]=0$$ $$\frac{df(x)}{dx}+f^2(x)-f(x)=\frac{1}{2x}$$ $$df(x)+f^2(x)-f(x)=\frac{1}{2x}dx$$
However I am unsure of how to continue/integrate over the left hand side. Any tips would be greatly appreciated!
I apologise in advance for any trivial mistakes I might have made, as I am not very familiar with differential equations yet. Thanks for your help!