(x³+y³)dx-3xy²dy=0,齐次方程的通解?dy/dx=(x³+y³)/3xy²=(1/3)[(x/y)²+(y/x)]=(1/3)[1/(y/x)²+(y/x)]令y/x=u,则y=ux,dy/dx=u+x(du/dx),代入上式得：u+x(du/dx)=(1/3)[(1/u&...