a surprising differential equation

don't want eat, want Chen Lu !

Bravo 👏

yeex!

YEET. Mic Drop

I got unreasonably uncomfortable when you dropped that marker without the cap on...

The joke in the end XD

Yeet
You're pretty funny guy.


You always zeem very happy too. I envy your enthusiasm

dy/yln(y)=dx
Integrate both sides
ln(ln(y))=x+c
y=e^e^(x+c)

Nice one!

❤

how would i know that y'/y is equal to ln(y)?

I got to an implicit solution with variable x so I was not expecting that looool

NOICE

Hmm...do I know enough to solve this? RHS reminds me of the antiderivative of ln(x)... x ln(x) -> ln(x) + 1; x ln(x) - x is that antiderivative, which I always have to rederive. Not sure that's helpful, though. y'' = y' ln(y) * y / y * y' = y'^2 ln(y) = y^2 ln(y)^3 this isn't working out. Wait... d/dx ln(y) = y' / y => d/dx ln(y) = ln(y) => z' = z where z = ln(y) => z = e^x | z = 0 => y = e^e^x | y = 1. d/dx e^e^x = e^e^x * e^x = e^e^x * ln(e^e^x) = e^e^x * e^x. d/dx 1 = 0 = 1 * ln(1) = 0. Ah, cool. In summary, y is one of { (\x -> e^e^x), const 1 }

Aha! I was surprised this was going this well. First, I hadn't watched any of the video to see the initial condition, and second, I missed the constant anyway, because I thought it would break it for some reason. Still, I think this is some ok "I should really be sleeping" math.

YEET!

What's there to be surprised at? A typical differential equation, quite easy to solve, it took less than a minute to solve it and less than one and a half of minute to show the solution in the video.

God you got me in tears at the end that was incredible 😂😂😂😂

i did some testing with the derivatives and found this strange series:

y' = y ln y
y'' = y ln y (1 + ln y)
y''' = y ln y (1 + ln y)^2 + y ln y^2
y'''' = (y ln y (1 + ln y)^2 + 4 y ln y^2) (1 + ln y) - y ln y^3
y''''' = (((1 + ln y)^2 + 6 ln y) (1 + ln y) + 4 ln y) y ln y (1 + ln y) + (3 ln y + 1) y ln y^2
evaluating them all at 0 gives: y, 2y, 5y, 15y, 52y, i wonder how this progresses?

I feel like I've just been rickrolled

HOW

Absolutely brilliant!

BRUH

Yeex!
dy/dx = y.ln(y)
ʃ1/{y.ln(y)} dy = ʃdx
let ln(y) = t, therefore, 1/y dy = dt
and so, ʃ1/t st = ʃdx
ln(t) = x + c
But t = ln(y) therefore,
ln(ln(y)) = x + c
as y(0) = e, c = 0
Hence,
ln(ln(y)) = x or y = e^e^x !
Pretty much the same thing, but this is how most of us may solve this in India.

Nice kitchen !

I don't understand please guys:
y=e^(ce^t)
So on the third line we have at right ln(y)=ln(e^(ce^t))=ce^t
On the left de have:
(ln(y))'=(ln (e^(ce^t))'=(ce^t)'=tce^t
That's différent from the right side but it's true if t is a variable like x but if t is a fonction like I think it's false I'm french so don't have the same conventionnal lettres. Thanks !

yeet

Me: im doing pretty well in math i bet differential equations wont be tha..
differential equations: yeet

Wait a minute. How did the fifth line of the solution come about?

Yeeet very funny. The double exponential pier tower , were the exponents negative , is the extreme value distribution of statistics ( Fisher and Tippet) whose moments are Bernoulli numbers . Another funny and keeps it simple video by the best math teacher I've ever witnessed , incl my college days . 😃👍

Sweet

I hope the meme potential in this blows up.

Best punchline in all of mathematics

Ok I’m doing the joke at the end on my first day back to in person teaching, it’s going to be a litmus test for how well the rest of the semester will go:D

Nice

My Math Professor randomly sent this to us

I got the same result :-)

eeeet

he's so adorable and precious

روز استاد مبارک .دکتر پیام عزیز. مرسی بخاطر تدرس تان

We must stop thees man. Before you know eet, people might think math ees fun.

y-squared equals yeet

What's the region where you're guaranteed to have a unique solution?

My thoughts during the video: "Hmm, why is he using 't' as the input of that function? Maybe it has some physical applicatio.....nevermind" :D

Wonderful.

Dr. Peyam is defiantly the best “friend” balckpenredpen used to tell us about in his videos…..Yeet

Knowing the solution, are there a way to obtain the differential equation?