Laplace transform to solve a nonhomogeneous equation

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Discussion Overview

The discussion revolves around the use of the Laplace transform to solve a nonhomogeneous differential equation, particularly in the context of initial conditions and whether they are appropriate for the problem type being addressed.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the applicability of the Laplace transform given the initial conditions s(x) and s(-x), suggesting that these may not be suitable for a nonhomogeneous equation.
  • Another participant notes that a first-order differential equation requires only one initial condition, implying that having two could lead to contradictions.
  • There is a suggestion that the problem may actually be a boundary value problem rather than an initial value problem, which could affect the use of the Laplace transform.
  • It is proposed that if the differential equation is a linear constant coefficient, the Laplace transform might still be applicable, although this is not definitively stated.
  • A later reply indicates that power series solutions may be necessary if the coefficients of the differential equation are non-constant, although this is presented as a guess due to the lack of specific details about the differential equation in question.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the problem (initial value vs. boundary value) and the appropriateness of the Laplace transform, indicating that multiple competing perspectives remain without a clear consensus.

Contextual Notes

The discussion lacks specific details about the differential equation in question, which may limit the applicability of the points raised. There is also ambiguity regarding the nature of the initial conditions and their compatibility with the problem type.

victor77
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Mod note: Moved from a Homework section
can i use the Laplace transform to solve a nonhomogeneous equation if
i have these Initial condition s(x) and s(-x)
 
Last edited by a moderator:
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Hi,
A first order differential equation only needs one initial condition, so the two you have might contradict each other.
A second order needs two. One per differential. So if you have two for the differentiation wrt x only, you are back to the previous problem. And you still don't have anything for ##{d\over dx}({d\over dx})##
 
victor77 said:
Mod note: Moved from a Homework section
can i use the Laplace transform to solve a nonhomogeneous equation if
i have these Initial condition s(x) and s(-x)

Looks like you have a boundary value problem not initial value problem. If your DE is a linear constant coefficient, I think you still can solve it with Laplace transform.
 
matematikawan said:
Looks like you have a boundary value problem not initial value problem. If your DE is a linear constant coefficient, I think you still can solve it with Laplace transform.

You have to use power series solutions, if the coefficients are non constant. This is just a guess, because you have not posted the DE you have questions on.
 

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