Solution of linear PDEs obtained using Laplace transform

Abstract

We would like to find the solution of PDEs obtained using Laplace transform. The solution of linear PDEs using Laplace transform has the advantage that an arbitrary constant is specifically displayed as an initial value. Of course, even if the Laplace transform used as a tool is replaced with many other Laplace-type transforms, the obtained result still holds. In addition, the solution of example 2 is obtained using ChatGPT and compared with the exact solution.