diff eq

[flint timber]

I don't understand why General solution is lambda/1+x and not exp(-(integral of 1/1+x))

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[flint timber]

It is an easy one

I just don't get it

[fathom pasture]

Ummm...

Just asking, what grade are you right now mate?

[flint timber]

I am not in US

Not the same shit

[fathom pasture]

Are you on High school mate?

[flint timber]

no haha

higher level

[fathom pasture]

So???

[flint timber]

I am in classe préparatoire aux grandes écoles PCSI

I don't have same classes as you

[fathom pasture]

...

[flint timber]

I told you

[fathom pasture]

Lemme guess...

[flint timber]

same as highest level of calculus, algebra, and analytics etc for you

[fathom pasture]

You're...in college?

[flint timber]

I am still in high school

just not an highschooler

lol

[fathom pasture]

Ohhh

I see

[flint timber]

I am studying in an highschool

doing a higher level than college maths

[fathom pasture]

That's good btw

[flint timber]

In france we call that a preparatory class for highest level school

you know Ecole polytechnique or even ENS Ulm

[fathom pasture]

You know mate...
Im still 9th grade 💀
But, after i looked around me...math is incredible! And fun!

[flint timber]

A highschooler could solve my shit

I just don't understand lol, my brain is fried

[fathom pasture]

Where did you get this question from?

[flint timber]

see I just solved my shit

I am a dumb fuck

Just understood

[flint timber]

bibmaths.net

What was the question you needed ?

euler identity ?

[fathom pasture]

Yes

[flint timber]

what don't you understand ?

[fathom pasture]

Im still studying about that

[flint timber]

not the answer I was looking for

[fathom pasture]

Ik

[flint timber]

what don't you get then

[fathom pasture]

I forgot...ummm...
Ouh. The Taylor

[flint timber]

?

[fathom pasture]

I just don't understand about taylor series

[flint timber]

that ?

[fathom pasture]

Yup

[flint timber]

it is a generalization of nth square root

for n> 1

and euler identity is when e =2

[fathom pasture]

Wait.

I just... remember something

[flint timber]

rest I can't explain, it is too high level for me

it goes into 4th dimension

[fathom pasture]

$e^x = \sum_{i = 0}^\infty \frac{x^n}{n!}$

[mortal bobcat]

ΛηοΣιμμυσ Ριδδληρ

[fathom pasture]

Do you know about this?

I just got it from my mind

Is it true?

[main kernel]

it's not I dont think

[flint timber]

it is

just did it ^^

[main kernel]

it's not, the general solution has a log term

[flint timber]

no

[main kernel]

$\dv{y}{x}+\frac{1}{1+x}y=\frac{1+\ln(1+x)}{1+x}$, integrating factor is $\mu(x)=\exp(\int\frac{1}{1+x}\dd{x})=1+x$, so $\dv{x}[(1+x)y]=1+\ln(1+x)$

[mortal bobcat]

Omegabet_

[main kernel]

hence $(1+x)y=\int 1+\ln(1+x)\dd{x}=x+(x+1)\ln(x+1)-x+C=(1+x)\ln(1+x)+C$

[mortal bobcat]

Omegabet_

[main kernel]

so $y=\ln(1+x)+\frac{C}{1+x}$, look at that log term

[mortal bobcat]

Omegabet_

[main kernel]

as for why you didnt get the log term in your general solution, you did something wrong.

[fathom pasture]

@main kernel what is dy & dx means?

[main kernel]

dy/dx is the derivative of y wrt x...

take calc1 before trying to solve ODEs

[main kernel]

also that has nothing to do with Taylor series tbh, it's just Vieta's results applied to z^n-1

also I assume the radio silence on your part is you digesting the solution given

[flint timber]

@main kernel

I got $\frac{C}{1+x}+(1+x)ln(1+x)}$

[mortal bobcat]

ProteinBuck
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[flint timber]

I don't know why I still have the 1+x

in factor

[main kernel]

idk either

cause I see no work

[flint timber]

not redacted tho

don't know if you will understand

[main kernel]

oh you're doing variation of parameters?

[flint timber]

Yes

I just suck damn

i don't get ittttt

[main kernel]

so you have $y_p(x)=\frac{1}{1+x}\lambda(x)\to \lambda(x)=(1+x)\ln(1+x)$

[mortal bobcat]

Omegabet_

[main kernel]

hence $y_p(x)=\ln(1+x)$ since $\frac{1+x}{1+x}=1$

[mortal bobcat]

Omegabet_

[main kernel]

the particular solution isnt just lambda, it's (1/(1+x))lambda in this instance

[flint timber]

yes

but so it is general + particular

hence lambda/1+x + (x+1)ln(1+x)

either it should be lmabda + ln(1+x)

i don't get why it is what you said

even tho it is true

[flint timber]

can you call to explain ?

[main kernel]

recall how variation of parameters works

[flint timber]

ok

[main kernel]

you find the homogeneous solution, which was $y_h=\frac{C}{1+x}$

[mortal bobcat]

Omegabet_

[flint timber]

yes

[main kernel]

then you guess that the particular solution is of the form $y_p=y_h\lambda$

[mortal bobcat]

Omegabet_

[flint timber]

yes

then derivate

then plug in equation

[main kernel]

to which the general solution is $y=y_h+y_p$

[mortal bobcat]

Omegabet_

[main kernel]

you found $\lambda=(1+x)\ln(1+x)$ and $y_h=\frac{1}{1+x}$

[mortal bobcat]

Omegabet_

[main kernel]

so what's $y_p$?

[mortal bobcat]

Omegabet_

[flint timber]

maths lore is cool, maths gameplay just sucks

let me do it all over again for the third time

third time's the charm

[main kernel]

you didnt do anything wrong in your working, you just plugged in lambda for your particular solution, not y_h*lambda

[flint timber]

@main kernel

[main kernel]

yeah, so what's the particular solution?

[flint timber]

Guess I should stop maths forever

[main kernel]

there you go

[flint timber]

How bad am I bruh

[main kernel]

and no lol, making a mistake doesnt mean you stop forever

[flint timber]

Good redaction ?

[flint timber]

Look how dumb the mistake is

[main kernel]

so?

[flint timber]

How can i pretend at high level failing at this

[main kernel]

cause higher level doesnt really do computations

[flint timber]

computation ?

[main kernel]

yeah, solving ODEs is computation

[flint timber]

Oh

That’s for physics

This ain’t pure maths

[main kernel]

or for computers

[flint timber]

I don’t do that in maths

i do pre hilbertian space

and shit like that

[main kernel]

pre hilbert spaces specifically seems like a weird niche but ok

[flint timber]

Wait

https://www.bibmath.net/ressources/index.php?action=affiche&quoi=mpsi/index

here is what I do

thats my program

[main kernel]

that's just a vector space w/ an inner product, you usually care about hilbert spaces in which the induced norm makes the space complete

ok yeah, just defining the notion of inner products

[flint timber]

I am still at really low level maths

I can’t afford doing mistakes like that that’s just why am disappointed

anyway, going back to that physics shit

[main kernel]

then you just take your time until the algorithms/steps are crystal

your mistake was just forgetting how the particular solution was constructed, the actual work was all correct

[flint timber]

what is your maths level

[main kernel]

Im going into my 4th year at uni

@flint timber forgot to ping w/ the reply