A Note on Laplace Transforms of Some Particular Function Types

TL;DR

This paper discusses specific Laplace transform pairs and extensions, providing methods to find transforms or inverses for functions involving implicit types, aiding in solving complex differential equations.

Contribution

It introduces new extensions to basic Laplace transform equations applicable to functions with implicit forms, enhancing transform calculation techniques.

Findings

Developed extended Laplace transform pairs.

Provided methods for implicit function transforms.

Facilitated solving complex differential equations.

Abstract

This article handles in a short manner a few Laplace transform pairs and some extensions to the basic equations are developed. They can be applied to a wide variety of functions in order to find the Laplace transform or its inverse when there is a specific type of an implicit function involved.