微分方程（x+1)dy/dx=y-y^2通解在线等,急RT

xdy+dy=ydx-y^2dx
xdy-ydx+dy=-y^2dx
(xdy-ydx)/y^2+dy/y^2+dx=0
d(-x/y-1/y+x)=0
通解为：-x/y-1/y+x=c

dy/[y(1-y)]=dx/(x+1)
两边积分：ln|y|-ln|1-y|=ln|x+1|+C
y/(1-y)=C(x+1)
y=C(x+1)/(C(x+1)+1)

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)