Solution of a special case of Abel's differential equation of the second kind

Write it as $$ \frac{dy}{dx}=\frac{A\,x+B+y}{y}. $$ The change of variable $A\,x+B=t$ transforms it into $$ A\,\frac{dy}{dt}=\frac{t+y}{y}, $$ a homogeneous equation.

Two changes of variables transform the non-linear ODE to an ODE on separable kind. The solution is expressed on implicite form :