Solving the logistic differential equation part 2 | Khan Academy

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Differential Equations on Khan Academy: Differential equations, separable equations, exact equations, integrating factors, homogeneous equations.
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[@Deuce1042]

For some reason vids like this never explain this but in case anyone was wondering, taking the reciprocal of both sides such that the left side of the equation is 1-(N/K)/N avoids a potential division by zero.

[@LariosGiveNoFucks]

I was having a hard time deriving this solution and getting it to the final form you had it in but now you made it so much easier. Thank you!!

[@CalrosACJ55]

3:40 Why, instead of simply multiplying by 1-(n/k), moving the terms with N to the left, factorizing N, and dividing, did you suddenly go into the line of thought where you use new constants? And should I approach all differential equations in this way? Is the form that you arrive at with your method somehow superior to the other one?

[@ronnielane6903]

I realize this video has been up for a long time now, but thanks anyway for the upload. I have used this logistic differential equation many times, but never understood it's derivation until now. Very cool stuff.

[@wilhelminamoore3113]

Always sounds like he's saying NFT

[@ridgemcghee2289]

At 8:18, why not multiply by K/K (instead of NoK / NoK)?
You end up with something simpler to work with and the terms even make sense:
N(t) = K / (1 + (K/No - 1))e^-rt)
Then, after setting K = 1000 and No = 100:
N(t) = 1000 / (1 + (1000/100 - 1))e^-rt)
N(t) = 1000 / (1 + 9e^-rt)
N(t) = 1000 / (1 + 9e^-.0205t)

[@nullheim]

Well actually I started to solve it on my own, and what I got at the end is N(t)=((KN.)/(e^(-rt)K+N.)), I checked my calculations didnt notice anything awkard, well may be I got miscalculated something and didnt realize that, but how so ?
NOTE: N. represents N sub-null

[@benjaminsmus8553]

We will call this logistic function and in future videos we will explore it more and see what it actually does

[@MegaPromQueen1]

When school starts back you're going to get so many more views.

[@XxTamiChuxX]

Why am I watching this?

[@slowfern]

Lifesaver!!

[@mmenta56]

FUCK THIS SCHOOL IS OUT

[@sshannon1948]

Ask not for whom the school bell tolls, it tolls for thee!!

[@okotray4577]

Yes, easy now. Also long enough

[@peter_roth_8812]

This is realy important. But what are you going to do when the actual population at a time t is much larger than it has to be according to this equation?

[@adamthornton7880]

If you start with a population above carrying capacity you will get negative population growth. N would asymptotically approach K from the topside.

[@peter_roth_8812]

Adam Thornton Thank you for your answer. Adam. I can see it now.. If N is larger than K then the growth of the function is negative because 1 - N/K is less than zero.

[@TraleeFair]

Its N nort not N knot.

[@prabinlamsal5125]

Its N nought bro. Nought means zero.