dy/dx=y(y-1),y(0)=0的特解

dy/dx=y(y-1)
(1/(y-1)-1/y)dy = dx
ln|(y-1)/y| = x+ C
y(0) =0
C=0
ln|(y-1)/y| = x
(y-1)/y = e^x
y(1-e^x) = 1
y = 1/(1-e^x)