- #1
ColdFusion85
- 141
- 0
How would one obtain a Fourier Transform solution of a non homogeneous heat equation? I've arrived at a form that has
\frac{\partial }{ \partial t }\hat u_c (\omega,t) + (\omega^2 + 1)\hat u_c (\omega,t) = -f(t)
My professor gave us the hint to use an integrating factor, but I don't see how this would work. If p(x) = (\omega^2 + 1), and q(x) = -f(t), then the integrating factor would be e^{\int(\omega^2 +1)dw}
Multiplying through by this would not give the usual integrating factor form of (..)' on the left hand side. Can anyone help?
\frac{\partial }{ \partial t }\hat u_c (\omega,t) + (\omega^2 + 1)\hat u_c (\omega,t) = -f(t)
My professor gave us the hint to use an integrating factor, but I don't see how this would work. If p(x) = (\omega^2 + 1), and q(x) = -f(t), then the integrating factor would be e^{\int(\omega^2 +1)dw}
Multiplying through by this would not give the usual integrating factor form of (..)' on the left hand side. Can anyone help?
