Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! 🙂 !! The Logistic Equation and the Analytic Solution. In this video, I find the analytic solution to the logistic differential equation.

Nguồn:https://nhaxehoanglong.com/

Thank you soo soo much for the vid!!!

Okay I found your channel when I was in algebra 2 and now I’m in calc and you still have clear and helpful videos for that, that’s pretty amazing. Thank you!

Thanks bro

I'm momentarily confused over where the dp at 4:38 came from ;-;

why do people choose to multiply by negative 1?

Simply the best. cheers

Thank u so much .👍👍

Crack!!!!!

congrats on 1 mil subs patrick

Just echoing what other are saying but this is excellent. Thank you.

Great derivation, but representation of the Logistic formula is hard to reconcile with other

generally presented version of the formula.

what the value of e

Very good video, thank you, but why would you but K and k?? That;s just mean

Hey man, thanks for the video! I know its old but could you explain why you remove the absolute and then say the A can be + or -?

THANK YOU

Ugh

This helps so much thank you!

The BIG K should replace to "M", so we would not mix up.

you're a hero! I couldn't thank you enough

Around in circles.

Thank you for this simple explanation! Unfortunately textbooks fail to understand that if they explained things like you just have – that it would build our confidence and help get our minds around more complex problems.

i love u thank u so much

Dude, At Khan Academy Sal tries to show how to solve the thing, too. However, for some reason he is not being all that clear about it and, according from what can be picked up from the comments, many people are left confused. You are doing so much better of a job here, so I suggest you send in this clip as a basis for improvement to K.A.!

I like how very clearly you explain what you are doing, this was a lot of help to me.

he said dp hehehe

you are totally better than my lecturer lol

what i can say is AMAYZING! 😀

Great and very helpful but… you should learn how to write with your right hand…

That would solve the problem of covering what has been just done 🙂

thank you so much! this was really helpful 🙂

Thank you for yet another brilliantly explained, concise video. So well explained – I had never done partial fractions before and it made everything so simple. Keep up the good work!!

@jukeboxheroes inverting the fraction (P/K-P) eliminates a potential future division by 0.

because (K-P)/P = K/P – 1 (better form?)

do u know how to do the second derivative of the solution?

It took me three watches to notice that you're left-handed

He did that to help with separating P from the equation at a later stage. But an answer can be obtained by various ways.

I tried solving for P(t) WITHOUT multiplying by (-1) and initially got this: [P/(K – P) = Ae^kt] –> Now in order to completely separate P, I'd have to take the inverse of both sides of this equation: [(K-P)/P = A.e^-kt] –> [(K/P) – 1 = A.e^-kt] –> P = K/(A.e^-kt+1), which is Patrick's solution. Hope that clears things out (:

and there we have it… /watch?v=nxs0WbkKZCk

I always get ln |P / K-P|

why is it important to flip this??? why is it important to multiply by -1???

PATRICK! please tell me WHY you multiplied by -1 at 5:55 !!!