微分方程（x+1)dy/dx=y-y^2通解在线等,急

题目

微分方程（x+1)dy/dx=y-y^2通解在线等,急
RT

答案

变量分离
dy/(y-y²)=dx/(x+1)
dy/y(1-y)=dx/(x+1)
[1/y+1/(1-y)]dy=dx/(x+1)
积分
ln/y/-ln/1-y/=ln/x+1/+c1
ln/y/(1-y)/-ln/x+1/=c1
ln/y/(1-y)(x+1)/=c1
C=±e^c1=y/(1-y)(x+1)
∴同解为：
y=c1(1-y)(x+1)