将原方程两边微分得d[xe^y+sin(xy)]=0→e^ydx+xe^ydy+cos(xy)(ydx+xdy)=0→移项
[xe^y+xcos(xy)]dy=-[e^y+ycos(xy)]dx整理→dy/dx=-[e^y+ycos(xy)]/[xe^y+xcos(xy)].
这种方法是最快最不易出错的.