If dydx=xy+yxy+x, then the solution of the differential equation is
y=xex+c
y=ex+c
y=Axex−y
y=x+A
∵dydx=y(x+1)x(y+1)⇒∫y+1ydy=∫x+1xdx ⇒∫dy+∫1ydy=∫dx+∫1xdx⇒y+lny=x+lnx+c⇒lnyx=x−y+c⇒yx=ex−y+c⇒y=xex−yec⇒y=Axex−y