Question

Solve the integro-differential for y(t)

y(t) + 3*int_{0}^{t} y(v)*sin(t-v)dv = t
in case the integral thinger doesn't work
y(t_ +3* the integral of [y(v)*sin(t-v)dv] = t
lower limit is 0. upper limit is t

Answer 1

fail. equations hurr:
\[y(t) + 3*\int\limits_{0}^{t} y(v)\sin(t-v)dv = t\]

Answer 2

subject is differential equations, section is convolutions

Answer 3

god, not that.

Answer 4

you supposed to be using laplace transform?

Answer 5

yessir

Answer 6

have a test in 5 hours lol. last thing i need to understand before i feel ready.

Answer 7

I think it's just
\[Y(s) +\frac{ 3Y(s) }{ s^2+1} = \frac{ 1 }{ s^2 }\]

Answer 8

i think there's supposed to be a sin(something) + something

Answer 9

I'm moving on in about 3 minutes lol. still get to do power and taylor series and dirac delta functions. yayyyyy lol

Answer 10

solve for Y(s) and inverse transform...

Answer 11

sec

Answer 12

gahhhh. im at y(t) = t - sin(t)*y(t)
the * is the convolution symbol

Answer 13

hmm I got (1/4)sin(2t) + t*(1/4)sin(2t))
the * is the convolution symbol

Answer 14

been a while since I've done these, though...

Answer 15

so \[Y = \frac{ 1 }{ s^2 } - (\frac{ 1 }{ s^2+1 })*(Y)\]

if that makes any sense

Answer 16

i have a feeling this test is gonna tank my grade haha

Answer 17

\[Y(s) = \frac{ s^2+1 }{ s^2(s^2+4) }\]
did you get that?

Answer 18

nada

Answer 19

i dont know what im getting yet lol. lemme roll w/ that for a sec tho

Answer 20

so using that i got 3sin(2t)/8 + t/4

Answer 21

how did you get to that point?

Answer 22

solved Y(s)+3Y(s)/(s^2+1)=1/s^2
for Y(s)

Answer 23

but how did you get 3sin(2t)/8 + t/4 ?

Answer 24

partial fraction decomp and then inverse LT

Answer 25

how did you get to this point lol

solved Y(s)+3Y(s)/(s^2+1)=1/s^2 for Y(s)

Answer 26

convolution in time domain is multiplication in s domain so L(sin(t)) *L(y(t))

Answer 27

yeah I see... would've have thought that wouldn't * work here, so I didn't try it..

Answer 28

kkkkkkk got it :)
<3

Answer 29

thanks for the help, onto power and taylor series!!! lol