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Troubles with Fourier Transform solution of the non-homogeneous wave equation.

  1. Nov 10, 2011 #1
    1. The problem statement, all variables and given/known data
    [itex]u_{tt} = c^2 u_{xx} + h(x)[/itex]
    [itex]u(x,0) = f(x)[/itex]
    [itex]u_t(x,0) = g(x)[/itex]


    2. Relevant equations
    http://cnx.org/content/m10099/latest/" [Broken]

    [itex]y = y_c + y_p [/itex]


    3. The attempt at a solution

    I have been able to solve the homogeneous equation and arrived at the d'Alembert Formula as expected. Where I'm stuck is with incorporating the particular solution. More specifically, I don't know how to handle it. None of the text books I have have any sort of an example on how to handle non-homogeneous PDEs when using Fourier Transforms to solve them. Am I wrong to have considered the solution to be a sum of the solution to the homogeneous problem and the particular solution? Honestly, even if someone had just a reference online to any non-homogeneous PDE solved with a Fourier Transform, I would be grateful.
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
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