Solving Nonhomogeneous Heat Equation with Fourier Transform

  • #1
ColdFusion85
142
0
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?
 

Answers and Replies

  • #2
ColdFusion85
142
0
Anybody?
 
  • #3
ramtin
6
0
The integrating factor is :
[tex]
e^{\int(\omega^2 +1)dt}
[/tex]

but I don't know what to do next
 

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