The solution of y1+x−1+sinydx+x+logex+xcosydy=0  is

ydx+yx⋅dx+sin⁡ydx+xdy+loge⁡xdy+xcos⁡ydy=0⇒(ydx+xdy)+y⋅dxx+loge⁡xdy+(sin⁡ydx+xcos⁡ydy)=0⇒d(xy)+dyloge⁡x+d(xsin⁡y)=0     integrating on both sidesxy+yloge⁡x+xsin⁡y=C