2dx/x=(1-2u)/(1-u+u^2)du
2dx/x=(1-2u)/[(u-1/2)^2+3/4] du
2dx/x=- d(u-1/2)^2/[(u-1/2)^2+3/4],这一步关键是将分子看成是(u-1/2)^2的微分.
积分：
2ln|x|+c1=-ln[(u-1/2)^2+3/4]
C/x^2=(u-1/2)^2+3/4
C/x^2=y^2/x^2-y/x+1
C=y^2-xy+x^2
(2x-y)dx+(2y-x)dy=0的通解
2dx/x=(1-2u)/(1-u+u^2)du
2dx/x=(1-2u)/[(u-1/2)^2+3/4] du
2dx/x=- d(u-1/2)^2/[(u-1/2)^2+3/4],这一步关键是将分子看成是(u-1/2)^2的微分.
积分：
2ln|x|+c1=-ln[(u-1/2)^2+3/4]
C/x^2=(u-1/2)^2+3/4
C/x^2=y^2/x^2-y/x+1
C=y^2-xy+x^2