In this paper, we have introduced the modified version of Sumudu and Laplace
transforms, namely Elzaki transform for solving differential equations with variable
coefficients which was not solved by Sumudu transform. It has been shown that
Elzaki transform is a very effective method for solving initial value problems
compared with Sumudu transform. In a large domain the accurate convergence of
Elzaki transform will be discussed in the coming research.