I want to solve the differential equation $y'y^2=y+xy'$. I notice that the differential is not in the general form of first order linear equations which is $y'+P(x)y=Q(x)$. In fact the above equation is not linear.
I read that I have to switch the dependent and independent variable of the problem and then the problem will turn into linear first order differential equation. I don't quite understand the concept of switching dependent and independent variable, can someone explain?