求解微分方程：[x-ycos(y/x)]dx+xcos(y/x)dy=0.
问题描述：
求解微分方程：[x-ycos(y/x)]dx+xcos(y/x)dy=0.
答
1-y/x*cos(y/x)+cos(y/x)dy/dx=0令y/x=u,则dy/dx=u+xdu/dx所以1-ucosu+cosu*(u+xdu/dx)=0cosu*xdu/dx=-1cosudu=-dx/x两边积分：sinu=-ln|x|+Cu=y/x=arcsin(-ln|x|+C)y=xarcsin(-ln|x|+C)