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Solving Nonhomogeneous Heat Equation with Fourier Transform

  1. Apr 24, 2008 #1
    How would one obtain a Fourier Transform solution of a non homogeneous heat equation? I've arrived at a form that has

    [tex]\frac{\partial }{ \partial t }\hat u_c (\omega,t) + (\omega^2 + 1)\hat u_c (\omega,t) = -f(t)[/tex]

    My professor gave us the hint to use an integrating factor, but I don't see how this would work. If [tex]p(x) = (\omega^2 + 1)[/tex], and [tex]q(x) = -f(t)[/tex], then the integrating factor would be [tex]e^{\int(\omega^2 +1)dw}[/tex]

    Multiplying through by this would not give the usual integrating factor form of (..)' on the left hand side. Can anyone help?
  2. jcsd
  3. Apr 24, 2008 #2
  4. Dec 2, 2009 #3
    The integrating factor is :
    e^{\int(\omega^2 +1)dt}

    but I don't know what to do next
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