dy/dx=-(x^2+2xy)/(xy)=-(x+2y)/y=-x/y-2令u=y/x,则y=xu,y'=u+xu'代入原方程：u+xu'=-1/u-2xu'=-1/u-2-u=-(u+1)^2/uudu/(u+1)^2=-dx/xdu*[1/(u+1)-1/(u+1)^2]=-dx/x积分：ln|u+1|+1/(u+1)=-ln|x|+c1ln|y/x+1|+1/(y/x...