- #1

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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?

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- #1

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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?

- #2

Defennder

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- #3

HallsofIvy

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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

Defennder

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

- #5

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

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

- #6

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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.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".

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

- #7

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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.

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

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

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