- #1

- 75

- 0

x' + x = T

where x is a function of T and x(0) = 5 and x(4) = 7

Or can you only solve initial value problems?

You should upgrade or use an alternative browser.

- Thread starter Alex6200
- Start date

In summary, the conversation discusses using a Laplace transform to solve a differential equation and the difference between initial value problems and boundary value problems. Some argue that Laplace transforms are overrated and other methods, such as variation of parameters, could be used to solve the given problem. However, some believe that Laplace transforms have their own unique benefits. The possibility of using Laplace transforms to solve endpoint value problems is also mentioned.

- #1

- 75

- 0

x' + x = T

where x is a function of T and x(0) = 5 and x(4) = 7

Or can you only solve initial value problems?

Physics news on Phys.org

- #2

Homework Helper

- 2,593

- 5

- #3

Science Advisor

Homework Helper

- 43,008

- 974

I've always felt that "Laplace transform" was over rated. It gives a very "mechanical" way of solving problems that could be done in other ways. A problem like the one given here, to me, cries out for "variation of parameters".

- #4

Homework Helper

- 2,593

- 5

Why is this a second order differential equation? It is x' and not x''.

- #5

- 75

- 0

x'' + x = T, or something along those lines.

My question is: can I use Laplace transforms to solve endpoint value problems?

- #6

- 75

- 0

HallsofIvy said:I've always felt that "Laplace transform" was over rated. It gives a very "mechanical" way of solving problems that could be done in other ways. A problem like the one given here, to me, cries out for "variation of parameters".

I really like Laplace transforms. There's just something really cool and dare I say - transcendental - about how discontinuous areas on the t domain become continuous on the s domain. Although I'd suppose that's true of the integration transform too.

Also, it kind of blows my mind how similar T and sin(T) are on the s-domain.

- #7

- 85

- 2

Agreed, the Laplace transform simply complicates matters more by introducing finding the inverse Laplace transform. There are much easier ways to solve ODE's and simpler ways of reducing PDE's.HallsofIvy said:

I've always felt that "Laplace transform" was over rated. It gives a very "mechanical" way of solving problems that could be done in other ways. A problem like the one given here, to me, cries out for "variation of parameters".

- #8

- 10

- 0

Laplace transforms, I think, solves exactly the same family of equations that the method of undetermined coefficients solves.

Share:

- Replies
- 1

- Views
- 231

- Replies
- 17

- Views
- 475

- Replies
- 5

- Views
- 1K

- Replies
- 1

- Views
- 980

- Replies
- 6

- Views
- 1K

- Replies
- 4

- Views
- 1K

- Replies
- 7

- Views
- 2K

- Replies
- 2

- Views
- 2K

- Replies
- 3

- Views
- 2K

- Replies
- 2

- Views
- 1K