/sci/ - Science & Math » Thread #10138228

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Anonymous Tue 13 Nov 20:48:31 2018 No.10138228 View Reply Original Report

Quoted By: >>10138234 >>10138238 >>10138245 >>10138257 >>10138272 >>10138273 >>10138276 >>10138281 >>10138389 >>10138415 >>10138526 >>10139245 >>10139381 >>10141215 >>10141246 >>10141290

If you can't solve this problem, you are too young to be on this board

Anonymous

Anonymous Tue 13 Nov 2018 20:49:59 No.10138234 Report

Quoted By:

>>10138228
Y=8

Anonymous

Anonymous Tue 13 Nov 2018 20:52:18 No.10138238 Report

Quoted By: >>10138239 >>10138249

>>10138228
And by "trivial", I mean solutions such as y=B

Anonymous

Anonymous Tue 13 Nov 2018 20:53:13 No.10138239 Report

Quoted By:

>>10138238
Y=8.

Anonymous

Anonymous Tue 13 Nov 2018 20:58:09 No.10138245 Report

Quoted By:

>>10138228
y=B/A_0

Anonymous

Anonymous Tue 13 Nov 2018 21:00:46 No.10138249 Report

Quoted By:

>>10138238
>"give an example"
>solve a problem
Sure.

Anonymous

Anonymous Tue 13 Nov 2018 21:03:38 No.10138257 Report

Quoted By: >>10138261

>>10138228
do your own homework nigger

Anonymous

Anonymous Tue 13 Nov 2018 21:05:29 No.10138261 Report

Quoted By: >>10138267 >>10138371 >>10139075

>>10138257
Not homework, I've been trying to find generalizations of this class of differential equation for fun and I thought I'd share the fun.

One type of solution:
A = [1,1,1,1,1,...]
B = 0
y(x) = sin(x)

Anonymous

Anonymous Tue 13 Nov 2018 21:07:24 No.10138267 Report

Quoted By: >>10138274 >>10139382

>>10138261
Oh wow. You're retarded. That's not a solution, that's an example

Anonymous

Anonymous Tue 13 Nov 2018 21:08:27 No.10138272 Report

Quoted By: >>10138355

>>10138228
I fucking hate this latex equation font. What's it called?

Anonymous

Anonymous Tue 13 Nov 2018 21:08:56 No.10138273 Report

Quoted By: >>10138275

>>10138228
>give an example
I hate this stuff.

Anonymous

Anonymous Tue 13 Nov 2018 21:09:41 No.10138274 Report

Quoted By: >>10138279

>>10138267
This is bait, right?

Anonymous

Anonymous Tue 13 Nov 2018 21:09:42 No.10138275 Report

Quoted By:

>>10138273
Where does it say to give an example?

Anonymous

Anonymous Tue 13 Nov 2018 21:09:45 No.10138276 Report

Quoted By: >>10138283 >>10139258

>>10138228
This can easily be solved with the Fourier transform.
$\sum_{n=0}^\infty A_n \frac{d^ny}{dx^n} = B \\<br />\sum_{n=0}^\infty A_n \left(2 \pi i \xi \right)^n \left( \mathscr{F}(y) \right) (\xi) = B \delta (\xi) \\<br />\left( \mathscr{F}(y) \right) (\xi) = \frac{B \delta (\xi)}{\sum_{n=0}^\infty A_n \left(2 \pi i \xi \right)^n} \\<br />y (x) = \mathscr{F^{-1}} \left( \frac{B \delta (\xi)}{\sum_{n=0}^\infty A_n \left(2 \pi i \xi \right)^n}\right) (x)<br />$

Anonymous

Anonymous Tue 13 Nov 2018 21:11:20 No.10138279 Report

Quoted By:

>>10138274
No, retard. Your question is phrased wrong

Anonymous

Anonymous Tue 13 Nov 2018 21:12:12 No.10138281 Report

Quoted By: >>10138283

>>10138228
>>10138228
Just take the Laplace transforms of both sides. If the Laplace transform of y is Y, you will have $\sum A_n s^n = B/s$ Therefore, $Y = \frac{B}{s(A_0 + A_1 s + A_2 s + ...)}$ This can be decomposed into a series of fractions of the form $\sum \frac{C_n}{(s-D_n)^n}$ which become terms of the form t^(n-1) exp(D_n * t)/(n-1)!. There you go op, your homework done.

Anonymous

Anonymous Tue 13 Nov 2018 21:13:31 No.10138283 Report

Quoted By: >>10138287

>>10138276
>>10138281
Based and redpilled

Again, not homework, I'm just curious

Anonymous

Anonymous Tue 13 Nov 2018 21:16:24 No.10138287 Report

Quoted By: >>10138294

>>10138283
>Based and redpilled
What? Do you know what redpilled means?

Anonymous

Anonymous Tue 13 Nov 2018 21:21:05 No.10138294 Report

Quoted By: >>10138302 >>10138337 >>10141244

>>10138287
Based and redpilled is used when you agree with an anon, it's not supposed to make sense. Are you autistic?

e.g.
Anon 1> I like hotdogs
Anon 2> Based and Redpilled

Anonymous

Anonymous Tue 13 Nov 2018 21:23:08 No.10138302 Report

Quoted By:

>>10138294
What are you agreeing with tho?

Anonymous

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Anonymous Tue 13 Nov 2018 21:40:18 No.10138337 Report

Quoted By: >>10138517

>>10138294
>Based and redpilled is used when you agree with an anon

You need to go back. Jesus fuck.

Anonymous

Anonymous Tue 13 Nov 2018 21:48:01 No.10138355 Report

Quoted By:

>>10138272
euler math probably

Anonymous

Anonymous Tue 13 Nov 2018 21:57:42 No.10138371 Report

Quoted By: >>10138508

>>10138261
>A = [1,1,1,1,1,...]
>y(x) = sin(x)
Been a while since I did analysis, but I don't think that converges...

Anonymous

Anonymous Tue 13 Nov 2018 22:09:44 No.10138389 Report

Quoted By:

>>10138228
e^cx+B/A_0, where c satisfies W(c)=An*c^n+...A0=0;
C may be complex.

Anonymous

Anonymous Tue 13 Nov 2018 22:22:47 No.10138415 Report

Quoted By:

>>10138228
Hmm, perhaps you can do it through finding radius of convergence of the sequence, and then get a and b from there? Just a guess

Anonymous

Anonymous Tue 13 Nov 2018 22:55:08 No.10138508 Report

Quoted By: >>10138522

>>10138371
y(x) when A=[1,1,1,1,1,1,1,1,...] and B=0 would be sin(x), which would mean the summation would equal:
sin(x)+cos(x)-sin(x)-cos(x)+... = 0

Anonymous

Anonymous Tue 13 Nov 2018 22:57:56 No.10138517 Report

Quoted By: >>10141111

>>10138337
based and redpilled

Anonymous

Anonymous Tue 13 Nov 2018 22:59:34 No.10138522 Report

Quoted By: >>10138524 >>10141272

>>10138508
okay lets see here. What do you think
1-1+1-1+1-1+1-1...
is equal to?

Anonymous

Anonymous Tue 13 Nov 2018 23:01:12 No.10138524 Report

Quoted By: >>10138552

>>10138522
It's more along the lines of a + b - a - b

Anonymous

Anonymous Tue 13 Nov 2018 23:01:32 No.10138526 Report

Quoted By:

>>10138228
>niggas can't recognize a taylor series anymore

Anonymous

Anonymous Tue 13 Nov 2018 23:09:53 No.10138552 Report

Quoted By: >>10138564

>>10138524
Low iq underage brainlet retard

Anonymous

Anonymous Tue 13 Nov 2018 23:14:01 No.10138564 Report

Quoted By: >>10141287

>>10138552
Brainlet or master troll? I'm well aware that:
a+b-a-b+... = (a+b)(1-1+1-1+...)
You just got trolled lolololol

Anonymous

Anonymous Wed 14 Nov 2018 02:32:58 No.10139075 Report

Quoted By:

>>10138261
that doesn't converge my dude

Anonymous

Anonymous Wed 14 Nov 2018 04:24:04 No.10139245 Report

Quoted By:

>>10138228
>summing infinitely many functions, not functions evaluated at a point, and expecting it to produce a numerical answer
mate either it diverges or converges to some function, if you wanna fuck around with your trig identity thing try a finite sum, say, "find all functions such that the sum from 1 to 4k is an integer, for a fixed integer k" or something
>you are too young to be on this board

Anonymous

Anonymous Wed 14 Nov 2018 04:29:13 No.10139258 Report

Quoted By:

>>10138276
How did you know how to do that?

Anonymous

Anonymous Wed 14 Nov 2018 05:25:24 No.10139366 Report

Quoted By:

Let A_k be the first non zero A, assume all derivatives larger than k is 0, then it's just A_k y^(k) = B, this can be solved with a monomial y = Cx^k, to get C solve A_k C k! = B, so

y(x) = B/(k!A_k) x^k

Anonymous

Anonymous Wed 14 Nov 2018 05:35:27 No.10139381 Report

Quoted By:

>>10138228
this is simply a linear constant coefficient ordinary differential equation with a constant forcing term; which is extremely easy to solve, as simply as solving a polynomial. am i missing something?

Anonymous

Anonymous Wed 14 Nov 2018 05:36:30 No.10139382 Report

Quoted By: >>10139399

>>10138267
the question asks for *a* y(x) you idiot, ie. an example

Anonymous

Anonymous Wed 14 Nov 2018 05:42:56 No.10139399 Report

Quoted By: >>10139420

>>10139382
Yes, for free A and B. Not for example A and B.

Anonymous

Anonymous Wed 14 Nov 2018 05:50:59 No.10139420 Report

Quoted By:

>>10139399
oooo, now i understand. its just the homogeneous solution plus B/A_0 then

Anonymous

Anonymous Wed 14 Nov 2018 23:32:32 No.10141111 Report

Quoted By:

>>10138517
Based and redpilled

Anonymous

Anonymous Thu 15 Nov 2018 00:25:43 No.10141215 Report

Quoted By:

>>10138228
Find the homogeneous solution using the system of differential equations trick, diagonalize the matrix using eigenvectors and/or generalized eigenvectors, and solve the diagonalized system with exponential functions, and then apply the inverse eigenvector basis matrix to get the homogeneous solution. Because y = B/A_n is a solution, and because this differential equation is linear, you can just add this to the homogeneous solution set, and you will have the set of solutions to this differential equation.

Anonymous

Anonymous Thu 15 Nov 2018 00:49:11 No.10141244 Report

Quoted By:

>>10138294
>based and redpilled is used as a sign of agreement

Anonymous

Anonymous Thu 15 Nov 2018 00:50:04 No.10141246 Report

Quoted By:

>>10138228
>If you want help with your homework, go to /wsr/ - Worksafe Requests.

Anonymous

Anonymous Thu 15 Nov 2018 00:59:20 No.10141272 Report

Quoted By:

>>10138522
-1/12

Anonymous

Anonymous Thu 15 Nov 2018 01:06:35 No.10141287 Report

Quoted By: >>10141293

>>10138564
kys retard

Anonymous

Anonymous Thu 15 Nov 2018 01:09:13 No.10141290 Report

Quoted By:

>>10138228
Game developer here. I don't even know what that large E stands for.

Anonymous

Anonymous Thu 15 Nov 2018 01:09:45 No.10141293 Report

Quoted By:

>>10141287
Lol you fell for my bait. Who's the retard now, retard?

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