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fourier transform of DE

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naspek

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hey there..
i've got question on fourier transform..
the question is....
maths.jpg


i've done until..

\[
\begin{aligned}
\widehat{y}=\frac{\widehat{f}}{s^2+a^2}\\
=\widehat{g}\widehat{f}
\]

is this my general solution..?
 
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naspek

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i've done the inverse..

F^-1[g^(k)] = g(x) = 1/ √2∏ ∫g^(k)e^ikx dk
.............................. = 1/ √2∏ ∫ 1/ (k^2 + a^2)e^ikx dk
...............................= √2∏ [(e^-a|x|) / 2a]

what's the next step?
 

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