Question

Need help with LaPlace transform y''-y=5*sin2t when given y(0)=0, y'(0)=6

Answer 1

I've gotten to \[2^2L(y)-6-y=5*\sin2t\]

Answer 2

but I think I'm stuck... that should say s^2 not 2^2

Answer 3

\[s^2L(y)-6-y=5*\sin(2t)\]

Answer 4

do you have the value of y'(0)?

Answer 5

yep y'(0)=6

Answer 6

I messed that all up.... it should be\[s^2L(y)-6-L(y)=10/s^2+4\]

Answer 7

yeah this is right

Answer 8

Ok so what do I do from there?

Answer 9

try to solve for L(y)

Answer 10

I thikn I would go \[s^2(L(y)-1)-6=10/s^2+4\]

Answer 11

err

Answer 12

ok I prefer to write L(y) as Y(s)

Answer 13

\[L(y)(s^2-1)-6=10/s^2+4\]

Answer 14

it should be :
\[Y(s)(s^2-1)={10 \over s^2+4} +6\]

Answer 15

then you divide each side by s^2-1 and then look up the transform on a table?

Answer 16

=>6s^2+34 = Y{s^2 - 1}

Answer 17

Im confused on where you got that thinker

Answer 18

take the LCM :)

Answer 19

= \[Y(s)={6s^2+34 \over s^2+4} . {1 \over s^2 -1}\]

Answer 20

sry :) missed the denominator :)

Answer 21

are you follwoing Scotty?

Answer 22

now i guess u may use partial fractions to solve further

Answer 23

1 sec I think so im writing it out

Answer 24

take your time.. I will be right back

Answer 25

try a way to write it back in time domain

Answer 26

Yep I got it, you were adding 6 into there.

Answer 27

Can I look up the laplace transform inverse for each and then combine them?

Answer 28

i guess its possible when there's addition there..here we have multiplication of terms...can u use partial fractions?

Answer 29

Forgot how to do those, you're talking about breaking it up right?

Answer 30

take , say, (A/s^ + 4)+(b/s^2 -1)

Answer 31

sry it is (A/s^2 + 4)+(b/s^2 -1)

Answer 32

mm ok
I got it now. Thanks guys... I'm sure I'm gonna post another one here in a min lol

Answer 33

I am back

Answer 34

I think there is something wrong

Answer 35

no I just ran what we had through my solver and it came up with the correct answer...

Answer 36

I mean the partial fractions

Answer 37

whats that?? u know it was 2 years back i studies Laplace transforms :):)

Answer 38

:)

Answer 39

Oh well the laplace transform before you get to the fractions are correct :)

Answer 40

^^
yeah I know :)

Answer 41

omg!! did i forget solving these?? lol

Answer 42

if that's all you want, then it's ok.. but if you want to fin the final solution for the differential equation by yourself, then you need to do the partial fractions

Answer 43

right

Answer 44

the point is that you want to write the expression we have for Y(s) in a form that is easy to be transformed back to time domain

Answer 45

I didn't learn the notation in form of Y(s) which seems to be the way most people learn it. Very annoying.

Answer 46

was my suggestion of no help ??

Answer 47

No you helped thinker. Thank you :)

Answer 48

it doesn't matter what notation you use as long as you understand it.

Answer 49

thnx :) @scott