xy'-y=0xdy/dx=ydy/y=dx/x两边同时积分得lny=lnx+lncy=cx.
xy'-y=0两边同除以y^2得(xy'-y)/y^2=0凑微分得(x/y)'=0积分得x/y=C即x=Cy
都是正确的,常规解法是一楼,特殊题目才用二楼!