The solution of the differential equation xdydx=y+xey/x is

The given equation can be written as⇒dydx=yx+ey/x     put y=vx then dydx=v+xdvdxv+xdvdx=v+ev   ⇒∫e−vdv=∫dxx    by variables separable⇒−e−v+c=log⁡x⇒e−y/x+log⁡x=c