You can solve the differential equation y' = cy - by^2, and write the solution in terms of generic c and b.
Then see how you should choose c and b to get y=2/(1+e^-t).
Hello,
I was wondering if anyone could help me with my logistic equation problem; the question asks me what logistic equation is solved by y=2/(1+e^-t).
If I take the derivative from above I get 2et/(e^t+1)^2, however I have no idea how to get it to the form y=cy-by^2. I know it has something to do with finding the residue and splitting the variables, but I am stuck.
Okay, I've rearanged it so that Ce^ct=2/(c(1+e^-t)-2b)) but I don't know where to go from there. I think I have to take the ln() of the left side and multiply it by 1/c, but I'm not sure where to go from there. Sorry I'm so slow, but this is strange as this question is done backwards from what we were taught.