How can I compute the inverse two-sided Laplace transform symbolically?
I know MATLAB has ilaplace[1], but that's just for a one-sided transform.
How can I compute the inverse two-sided Laplace transform symbolically?
I know MATLAB has ilaplace[1], but that's just for a one-sided transform.
Unfortunately, you cannot calculate inverse two-sided Laplace transform by MATLAB. Because there are at least two reasons:
$1.$ MATLAB has not defined the functions for calculating inverse two-sided Laplace transform.
$2.$ Inverse one-sided Laplace transform is unique, but inverse two-sided Laplace transform is not unique. The reasons are explained in $\mathcal{B}^{-1}_{s\to x}\{e^{as^2+bs}\}$ and $\mathcal{L}^{-1}_{s\to x}\{e^{as^2+bs}\}$ , where $a\neq0$ .