There are many applications for the Laplace transform, including transforming types of differential equations. This comes up often in electronics where you have time-varying components like ...

Instead of having to solve a differential equation, you can perform a Laplace, solve using common algebra, and then do a reverse transform to get the right answer.

The transform is expressed in terms of the gamma and confluent hypergeometric functions. Using a simple Ito transformation and standard results on hitting times of diffusion processes, the transform ...

In this paper we adopt the perturbation approach of Landriault, Renaud and Zhou (2011) to find expressions for the joint Laplace transforms of occupation times for time-homogeneous diffusion processes ...