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Discontinuous driving function

  1. Jun 2, 2010 #1
    I have been studying LaPlace Transforms and I have learned how they are used to solve DE's with discontinuous driving functions, which is certainly interesting but I was wondering is it possible to solve the same DE's using other methods such as Undetermined Coefficients or Variation of Parameters(and how would it be done)?

    I have an idea of how you might be able to so, solving each continuous DE separably then adjusting the constants so the graphs meet consecutively but I don't know if this is correct.
  2. jcsd
  3. Jun 2, 2010 #2
    Yes it is. but it is very tedious.

    As a side note, the characteristic polynomial of a homogenous linear ODE is the same as the denominator of the Laplace transform. This is no coincidence.
  4. Jun 7, 2010 #3
    So how would you go about doing it?

    I was also wondering about why the characteristic polynomial shows up, to be completely honest I don't have a great understanding of LaPlace Transforms beyond them being a transform and something that is used to solve linear DE IVP's.
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