求dy/dx=y(y-1)的通解

问题描述:

求dy/dx=y(y-1)的通解

dy/dx=y(y-1)
dy/[y(y-1)]=dx
∫dy/[y(y-1)]=∫dx
∫dy/(y-1)-∫dy/y =∫dx
ln(y-1)-lny=x+C
(y-1)/y=Ce^x
1-1/y=Ce^x
y=1/(1-Ce^x)