Solving the logistic differential equation part 2 | Khan Academy

Differential Equations on Khan Academy: Differential equations, separable equations, exact equations, integrating factors, homogeneous equations.

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[Deuce]

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!!

[ronnielane]

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.

[CalrosACJ]

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?

[ridgemcghee]

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)

[benjaminsmus]

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

[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

[peter_roth_]

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?

[wilhelminamoore]

Always sounds like he's saying NFT

[MegaPromQueen]

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