You are Here: Home

# How to they get to this equation? (Integral representation for differential equation)

Maths and statistics discussion, revision, exam and homework help.

Announcements Posted on
Find out how cards are replacing warnings on TSR...read more 03-12-2013
1. How to they get to this equation? (Integral representation for differential equation)
I'm trying to understand how to use Laplace method to find solutions to ODEs. How do they use the correspondence rules (6.24) below to get from to ?

Last edited by TheEd; 11-04-2012 at 19:43.
2. Re: How to they get to this equation? (Integral representation for differential equat
**** I should be revising this.
3. Re: How to they get to this equation? (Integral representation for differential equat
Apply the "trick" in (6.23) to the product . Then use that result in your 3rd-last eqn.

You should be able to get the middle term, .

Does that help?
Last edited by steve10; 11-04-2012 at 21:20.
4. Re: How to they get to this equation? (Integral representation for differential equat
(Original post by steve10)
Apply the "trick" in (6.23) to the product . Then use that result in your 3rd-last eqn.

You should be able to get the middle term, .

Does that help?
How have they obtained (6.23)? What have they integrated by parts?
5. Re: How to they get to this equation? (Integral representation for differential equat
For (6.23), the IBP rule is,

Call the that you are working with in your post as in the IBP formula, with the term being (I imagine) the boundary term(s) that vanishes.

Can you see now how (6.23) is got ?

I'm off to watch the Apprentice now. Back in an hour.
6. Re: How to they get to this equation? (Integral representation for differential equat
If you put and in the IBP formula don't you get:

7. Re: How to they get to this equation? (Integral representation for differential equat

Writing the IBP formula as,

Now let and , then we get

Here the boundary term, is assumed to be zero, giving,

8. Re: How to they get to this equation? (Integral representation for differential equat
Sorry, I think I must have gotten mixed up with u's and v's and IBP. I gave you some bad info on post #5. Please ignore that post.

9. Re: How to they get to this equation? (Integral representation for differential equat
(Original post by steve10)

Writing the IBP formula as,

Now let and , then we get

Here the boundary term, is assumed to be zero, giving,

Thanks. I get where the equation comes from now but I don't really get the 'correspondence' things .
10. Re: How to they get to this equation? (Integral representation for differential equat
Well, to be honest, I don't fully understand (6.24), but I can get the 2nd last eqn in your post. Give me few minutes.
11. Re: How to they get to this equation? (Integral representation for differential equat
Using the method in my post #7, we can get,

Now, and

So, becomes

i.e.

## Step 2: Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank

this is what you'll be called on TSR

2. this can't be left blank

never shared and never spammed

3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
1. By completing the slider below you agree to The Student Room's terms & conditions and site rules

2. Slide the button to the right to create your account

You don't slide that way? No problem.

Last updated: April 12, 2012
Study resources