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# Laplace Transform/Final value theorem issue watch

1. Yo,

I basically have this question: 5. (a) Use the final value theorem to determine the value of y(∞), without actually solving the ODEy'+y=1, y(0) = 0
The Laplace transform of the ODE is: sG(s)+G(s)=1/s G(s)=1/s(s+1)

I know the answer is 1, I've solved the ODE and got the answer as 1 (when t approaches infinity) however G(0)=infinity, which can't be right, what have I done wrong?
2. (Original post by zooloowarrier)
Yo,

I basically have this question: 5. (a) Use the final value theorem to determine the value of y(∞), without actually solving the ODEy'+y=1, y(0) = 0
The Laplace transform of the ODE is: sG(s)+G(s)=1/s G(s)=1/s(s+1)

I know the answer is 1, I've solved the ODE and got the answer as 1 (when t approaches infinity) however G(0)=infinity, which can't be right, what have I done wrong?
I have not looked at this with pen and paper

the initial/final value theorem says

Limit (sf(s)) as s tends to zero equals F(t) as t tends to infinity

or

Limit (sf(s)) as s tends to infinity equals F(t) as t tends to zero

I will look at it later but
take the transform
then take limits as sf(s) tends to 0
might require some manipulation
3. (Original post by TeeEm)
I have not looked at this with pen and paper

the initial/final value theorem says

Limit (sf(s)) as s tends to zero equals F(t) as t tends to infinity

or

Limit (sf(s)) as s tends to infinity equals F(t) as t tends to zero

I will look at it later but
take the transform
then take limits as sf(s) tends to 0
might require some manipulation
Thanks, I'll give it another go
4. (Original post by zooloowarrier)
Thanks, I'll give it another go
Just finished dinner
it is actually a few lines
5. (Original post by TeeEm)
Just finished dinner
it is actually a few lines
I've gone over it twice now and still getting the same thing :/
1/s(s+1) definitely tends to infinity so I must have gone wrong with the actual transform but I can't see where
6. (Original post by zooloowarrier)
I've gone over it twice now and still getting the same thing :/
1/s(s+1) definitely tends to infinity so I must have gone wrong with the actual transform but I can't see where
give me 5 minutes to write it
7. (Original post by TeeEm)
give me 5 minutes to write it
Thanks for your help
8. (Original post by zooloowarrier)
I've gone over it twice now and still getting the same thing :/
1/s(s+1) definitely tends to infinity so I must have gone wrong with the actual transform but I can't see where
you should really post maths in the maths room
9. (Original post by TeeEm)
you should really post maths in the maths room
I'll keep that in mind for the next time
10. (Original post by zooloowarrier)
I'll keep that in mind for the next time
here it is
Attached Images

11. (Original post by TeeEm)
here it is
My bad, I didn't read/apply the theorem properly.

Thank you for your help!
12. (Original post by zooloowarrier)
My bad, I didn't read/apply the theorem properly.

Thank you for your help!
never mind

all the best

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