I have heard it said that the Laplace transform has "many applications". But the only "applications" that I ever came across are those that require one to solve either some kind of differential equation.
Can you provide an application of the transform, where the transform of the function allows one to solve a problem, but which is not differential equation related.
For example, the Fourier transform has applications to signal processing, where one sends/receives signals by transforming and inverting them afterwards. This application with the Fourier transform has no interest in any differential equation solution. Is there a similar application for Laplace?