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#1 2013-12-16 18:47:22

ammar
Member
Registered: 2013-12-16
Posts: 69

Laplace differential equation

Q.1     y'' -(1-t)y'+y=sin(2t)

where y(0)=y'(0)=5
                           t
Q.2     y''+[sin(t)∫exp(t)*sin(lnt)dt]y'+y=sinh(t)
                       5
where y(0)=y'(0)=2

Last edited by ammar (2013-12-17 06:01:09)

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#2 2013-12-17 01:13:40

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Laplace differential equation

Hi ammar;

The first one gets an answer that is messy, it involves the Error function. The second one I can not read. What do you want to do with these? How do you want them solved?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#3 2013-12-17 03:05:19

ammar
Member
Registered: 2013-12-16
Posts: 69

Re: Laplace differential equation

I want solved using Laplace transform to solve differential equations, please any help  I need solution of it as soon as possible

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#4 2013-12-17 03:17:01

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: Laplace differential equation

Hm, M gets this for the second DE:


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
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#5 2013-12-17 03:26:28

ammar
Member
Registered: 2013-12-16
Posts: 69

Re: Laplace differential equation

Any information about the way of solution

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#6 2013-12-17 03:33:46

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Laplace differential equation

Is  y' = dy/dt


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#7 2013-12-17 03:42:00

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Laplace differential equation

kaswat 478, please start a new thread for your question.

Please start a new thread, this one is for the Laplace transform.

Hi ammar;

Have you seen this page on how to do a Laplace transform of a DE?

http://en.wikipedia.org/wiki/Laplace_tr … ferential_


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#8 2013-12-17 03:48:01

kaswat478
Member
Registered: 2013-12-17
Posts: 2

Re: Laplace differential equation

I am sorry for that! One thing though, I am not sure how. How do you start a new thread?

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#9 2013-12-17 03:51:13

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Laplace differential equation

Okay, go into the Help Me! thread and on top you will see Post New Topic.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#10 2013-12-17 04:59:21

ammar
Member
Registered: 2013-12-16
Posts: 69

Re: Laplace differential equation

Yes, I know it but how to solve it if the function f(t)  multiply by f(s)

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#11 2013-12-17 05:01:30

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Laplace differential equation

Using the method of Laplace Transforms still is getting the same solution.

Have you copied the problems correctly?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#12 2013-12-17 05:56:39

ammar
Member
Registered: 2013-12-16
Posts: 69

Re: Laplace differential equation

Yes ,  I solved the first equation but with out result and I need to see other solution or another problems like this

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#13 2013-12-17 06:00:26

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Laplace differential equation

The Laplace transform leads to another DE. That should be obvious because of the non constant coefficient for one of the terms.
The answer is large and it is doubtful you could have solved it by hand.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#14 2013-12-17 06:04:08

ammar
Member
Registered: 2013-12-16
Posts: 69

Re: Laplace differential equation

at L[ty'] I get y''(s) and stopped ,,, sorry just sin(2t) not sin(25)

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#15 2013-12-17 06:08:45

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Laplace differential equation

I suspected there were mistakes, now how about that (1-t)?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#16 2013-12-17 06:12:35

ammar
Member
Registered: 2013-12-16
Posts: 69

Re: Laplace differential equation

I think it solved by definition of Laplace

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#17 2013-12-17 06:19:49

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Laplace differential equation

This is what Mathematica gets:

I do not think you are going to get that using Laplace.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#18 2013-12-17 06:29:57

ammar
Member
Registered: 2013-12-16
Posts: 69

Re: Laplace differential equation

http://lpsa.swarthmore.edu/LaplaceXform/FwdLaplace/LaplaceProps.html#Second_
look at First Derivative it the same way to solve the question

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#19 2013-12-17 06:34:10

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Laplace differential equation

Look on the bottom, at tf(t) the Laplace transform yields a derivative. That is why it leads to another DE.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#20 2013-12-17 06:40:14

ammar
Member
Registered: 2013-12-16
Posts: 69

Re: Laplace differential equation

Yes , but this equation is tf'(t)....

I'll upload my solution when I end

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#21 2013-12-17 06:41:31

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Laplace differential equation

Did you plug it back in to the DE to check it?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#22 2013-12-17 07:05:38

ammar
Member
Registered: 2013-12-16
Posts: 69

Re: Laplace differential equation

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#23 2013-12-17 07:27:52

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Laplace differential equation

You are leaving an integral in your answer. That is not considered solving the DE.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#24 2013-12-17 07:37:07

ammar
Member
Registered: 2013-12-16
Posts: 69

Re: Laplace differential equation

Yes, that were I stopped , if you can complete it or give me same examples I would be grateful to you

smile

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#25 2013-12-17 07:41:19

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Laplace differential equation

Not all DE's have simple solutions, most do not. I would give examples where the La[place transform got the answer not one where it does not.
Where does this problem come from?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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