Something's wrong here...

[@steve112285]

Since the solution to cos(x)=y is x=(+ or -)arccos(y)+2*pi*k, I'm thinking you need a 'plus or minus' in front of the -x-pi/2.

[@沈博智-x5y]

yeah. truth is x(t) = Ae^((+ or - )t) + 2npi - pi/2 when you take this into consideration. plugging it back in, you do get the equation to work still (even for the + case)

[@crazydog1750]

My main takeaway from all the experience I’ve ever had with differential equations is that if you simply guess that the solution is some variation of the exponential equation, you’ll probably be correct.

[@justkarl2922]

The moment when you forgooot how inhomogenius ode and variation of constants work :,,,,,,,,,ccccccc

[@JacquesRGAO]

however, -sin(x)=cos(-pi/2-x) or cos(pi/2+x) as cosine function is even, thus the o.d.e. to be solved is x'=2kpi \pm pi/2 \pm x (:

[@shreeniketupasani1957]

nice video... love the advent calendar series

[@mr.inhuman7932]

Nearly got through the Advent Calender! Keep up the work!

[@timhaines3877]

That equation could also be written cos(x') = (cos(x))' which feels like even more of a "freshman's dream".

[@PapaFlammy69]

yeah!

[@moustachescarz]

but that produces and additional x’ on the rhs

[@JavIkVR]

another weird cursed problem was solved🚬🗿

[@auseziegieteursucraineiwst3680]

How about integral sin(dx)

[@crazydog1750]

I would LOVE to see a step-by-step solution to this.

[@AriosJentu]

It’s not as hard, as like e^(dx). Just like inverse operation of exponential or trig derivative. We can use power series, as usual, to create close form for that

[@KingGisInDaHouse]

$sin(dx)=$[Lim h->0 (sin h)/h]dx=$1dx=x+C or use the engineering approach of sin h≈h for small or infinitesimal values.

[@bridgeon7502]

5:14 how come you can cancel the dt's?

[@fullfungo]

It’s the opposite of the chain rule: df/dt = df/dx•dx/dt You can look up “Integration by substitution” on Wikipedia. It contains a complete proof.

[@ultrio325]

it's called magic

[@海伯庵]

Has Papa Flammy finally integrated e^(x^2) yet? Or is he being an engineer about it?

[@PapaFlammy69]

several times ^^

[@potatadiggary1125]

Hi can anyone link where he has proven this 5:17 rigorously? I can’t seem to find it

[@chirbirbek9207]

en.m.wikipedia.org/wiki/Logarithmic_derivative

[@sierpinskibrot]

Great video great explanation

[@trwn87]

Neat differential equation! But how about “x = cos x”? The result is an irrational (and even transcendent!) number that might be worth a mention on your channel. :D

[@PapaFlammy69]

already done :)

[@trwn87]

@@PapaFlammy69 Okay, then you were ahead of me. But maybe you can take that, make it 10 times harder and then show it off. :D

[@trwn87]

@@PapaFlammy69 And I just realized, you ay have probably done the derivative of x^x before, but can you take the NTH derivative of it in general? No recursion allowed!

[@White-uq9fr]

​@@trwn87 Just use the Faà di Bruno's formula for exp(x*lnx) and then the Leibniz rule for x*lnx.

[@sudhamishra6596]

"The Hindu religion is the only one of the world's great faiths dedicated to the idea that the Cosmos itself undergoes an immense, indeed an infinite, number of deaths and rebirths. It is the only religion in which the time scales correspond to those of modern scientific cosmology. Its cycles run from our ordinary day and night to a day and night of Brahma, 8.64 billion years long. Longer than the age of the Earth or the Sun and about half the time since the Big Bang." “Most cultures imagine the world to be a few hundred human generations old. Hardly anyone guessed that the cosmos might be far older but the ancient Hindus did,” "It is the only religion in which the time scales correspond, to those of modern scientific cosmology" ~ CARL SAGAN (famous astronomer, cosmologist)

[@Happy_Abe]

Proven the shit!

[@edmundwoolliams1240]

You didn't "prove the shit" out of it, because you didn't differentiate e^-t the way that a 'real man' would.

[@faustodegrassi6132]

Interesting

[@hanskywalker1246]

Versteh ich nicht

[@creativename.]

very early