Solving the Verhulst Equation: Where Did My Calculation Go Wrong?

[asdf1]

for the following question:
y`-Ay=-By^2

my problem:
Suppose u=y^(-1)
so u`=-y^(-2)y`=B-Au
so du/(B-Au)= dx
=> B-Au=ce^x
=> u=(B-ce^x)/A
so y=1/u=a/(B-ce^x)

however, the correct answer should be y=1/[(B/A)+ce^(-ax)]
does anybody know where my calculations went wrong?

 

[hotvette]

so u`=-y^(-2)y`=B-Au

Take a look at this step again. I think one of the terms has the wrong sign.

 

[asdf1]

i see~
thanks!