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/sci/ - Science & Math

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15103017 No.15103017 [Reply] [Original]

How the fuck is this within the scope of an introductory differential equations class? How do you even begin to approach solving this?

>> No.15103052

>>15103017
Just integrate it twice lmao

>> No.15103055

>>15103017
Write a characteristic equation

>> No.15103059

>>15103017
>Find homogeneous solution (easy).
>Find particular solution for the summand.
>Take the sum of all the particular solutions.

>> No.15103068

>>15103055
>>15103059
The homogenous solution is trivial to find. But how do you find a particular solution of a series?

>> No.15103079

>>15103068
I literally told you, you retard.

>> No.15103088

>>15103017
x = sum a_n sin(nt)
Then look up the meaning of series orthonormality

>> No.15103147

>>15103017
OP, I teach myself math and physics while working the idle graveyard shift at a gas station, and even I can solve that.
Take the Ramanujan pill, man.

>> No.15103163

Undetermined coefficients everyone here is retarded.

>> No.15103165

>>15103163
Holy shit, you're dumb.

>> No.15103368

Probably a sum of sinusoids

>> No.15103372

Maybe use the superposition principle ?

>> No.15103390

sin''x=-sin x

So ez

>> No.15103453

x(t) = x_hom + x_part

x_hom is the solution of x" + 1/25x = 0
which is found by looking at the roots of

x^2 + 1/25 = 0
x 1,2 = +/- 1/5i (complex)
so the solution x_hom is
Acos(1/5t) +Bsin(1/5t)

for x_part we find it as follows
if y1 is the solution to x" + 1/25 = u1 = sin(t)
y2 is the solution to x" +1/25 = 2 = 1/2sin(2t)
...
then
sum(y1+y2+...) is the solution to
x" +1/25 = sum(u1 +u2+...)

so find the first few solutions and then sum them up that will give the x_part solution
then the solution to the BVP is x_h + x_part.

>> No.15103517

>>15103453
Lrn2latex fgt

>> No.15103523

>>15103163
You know, if you propose a method to solve a problem, maybe start by trying it yourself to see if it actually works

>> No.15103549
File: 764 KB, 1x1, sumsin_diffeq.pdf [View same] [iqdb] [saucenao] [google]
15103549

See pdf.

>> No.15103870

>>15103549
cute

>> No.15104170

>>15103549
is this the new lmgtfy?

>> No.15104196

>>15103549
kek
got lazy with the prose at the end tho

>> No.15104205

>>15103017
It's a Fourier series. Solve for the coefficients. Have you not been attending classes?

>> No.15104292

>>15103549
thanks anon

>> No.15104858

>>15103549
based anon, but homework posters should get no mercy

>> No.15104871

>>15103549
baZed

>> No.15105184
File: 663 KB, 1421x957, NJWW.png [View same] [iqdb] [saucenao] [google]
15105184

>>15103017
>an infinite of infinites
Utter nonsense

>> No.15105189
File: 95 KB, 978x1200, GC.jpg [View same] [iqdb] [saucenao] [google]
15105189

>>15103163
Variation of parameters is a better approach here.

>> No.15107293

bump

>> No.15107449

>>15103549
Lol, come on, I already told him how to do it in
>>15103088
You shouldn't make it that obvious

>> No.15107751

>>15103549
Thank you for the review.

>> No.15107844

>>15103017
Why don't you just visit your professor during his office hours?