generally we know that both Fourier transform and Laplace transform both is used to solve differential equation,first of all let us recall both form,first Fourier transform:
some times instead of $-2*\pi*f$,it is written $\omega$,and we know also Laplace transform
in some case low bound starts $-\infty$, and we know that
$s=\sigma+\omega*t$ ,which means that Fourier transform is a special case of Laplace when $\sigma=0$
but both methods is used to solve differential equation,my question us following how could i guess which method should i used in given concrete example?Laplace transform is used to transform differential equation into algebraic equation which simplify things,but what about Fourier transform?what it's goal in solving differential equation?