HUBUNGAN ANTARA TRANSFORMASI LAPLACE DENGAN TRANSFORMASI ELZAKI

Abstract

Laplace transform is a transformation method used to solve differential equations. The Laplace transform was first introduced by Pierre Simon Marquas De Laplace, a French mathematician and a professor in Paris. In addition to the Laplace transform, there is also a transformation of the Elzaki transformation which is a special transformation of the Laplace transform. The Elzaki transformation was introduced by Tarig M. Elzaki to find a solution of ordinary differential equations. Generally these two transformations are used to solve linear differential equations, in the transformation process using integral with a range from 0 to ∞. Unlike Elzaki's transformation, the Laplace transform does not have integral integral operators with 𝑣𝑣 variables. The purpose of this research is to find the relationship between Laplace transformation with Elzaki transformation. The result of this research indicates that Elzaki's transformation of a function 𝑓𝑓 (𝑡𝑡) has a relationship with Laplace transformation ie 𝑇𝑇 (𝑣𝑣) = 𝑣𝑣𝑣𝑣􁉀1𝑣𝑣􁉁 while for Laplace transformation 𝐹 (𝑠𝑠) = 𝑠𝑠𝑠 􁉀1𝑠𝑠􁉁 with 𝑇𝑇 (𝑣𝑣) and 𝐹 (𝑠𝑠) are the Elzaki and Laplace transforms of 𝑓𝑓 (𝑡𝑡), respectively. Based on the above relationship we can obtain the Elzaki transformation properties corresponding to the Laplace transform.