Solution of the differential equation dydx=2x−y+1x+y+2 is

Given that dydx=2x−y+1x+y+2⇒(x+y+2)dy=(2x−y+1)dx⇒xdy+(y+2)dy=2xdx−ydx+dx⇒xdy+ydx+(y+2)dy=2xdx+dx⇒d(xy)+(y+2)dy=2xdx+dxIntegrating on both sides⇒xy+y22+2y=x2+x+C Therefore, the correct answer is (4).