dy/dx=(ycos(y/x)-x)/(xcos(y/x))=y/x-sec(y/x)
设u=y/x,y=ux,dy/dx=u+u'x
即u'x=-secu
cosudu=-dx
sinu=-x+C
即通解为sin(y/x)+x=C
求解微分方程(x-ycosy/x)dx+xcosy/xdy=0
dy/dx=(ycos(y/x)-x)/(xcos(y/x))=y/x-sec(y/x)
设u=y/x,y=ux,dy/dx=u+u'x
即u'x=-secu
cosudu=-dx
sinu=-x+C
即通解为sin(y/x)+x=C