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Abstract
Differential equation is such a field which useful in not only Mathematics but in other Mathematical sciences. There are many traditional methods for solving ordinary and partial differential equations with initial conditions in literature.[ 6]. Laplace transform is the integral transform which is applicable in solving ordinary and partial differential equations [1] .This transform is also applicable in engineering sciences [6]. There is one more integral transform namely Sumudu transform proposed by Gamage K. Watugala to solve differential equations in 1993 [3].Most of the derivations in Mathematical sciences are in the form of ordinary or partial differential equations which we can solve by applying these integral transforms. In this chapter we have applied both transforms Laplace and Sumudu for obtaining solution of ordinary linear differential equations of second order with constant and variable coefficients. Finally we have compared Laplace transform method &Sumudu transform method for solving Ordinary differential equations with variable coefficients.