Hello. I am trying to figure out why y=0 is an answer in the logistic differential equation. I found a proof where they differentiate d(0)/d(x)=0 <=> 0=0, but can you differentiate d(0)/d(x), is that even legal?
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I find another proof where they say that y=0 is the lower asymptote and y=b/a is the top asymptote. I find this proof to be correct.
Can anyone tell me why y=0 would ever be an answer?
A link would also be helpfull if anyone has one
If anyone reads this, I found the answer next day.
The differential equation solution for logistic groth is y=(b/a)/(e^(-bx)*C+1) OR y=0.
y=b/a is part of the first solution (when C=0).
y=0 is whenever b=0.
Which means there are 3 kinds of solutions. y=0 (a straight line)
y=b/a, also a straight line, but at the top of your graph. It is the maximum your equation can have.
and the final solution is the sigma curve.
It helps to look at how a population of a certain group of humans grow.
(if y=0, then there are no people and ofcause there will never be born any new...)
(if y=b/a, this means the maximum amount of people alllow/possible has been reached)
(if the last solution is the case, then the sigma curve is your answer)