A method for finding the general solution of the LODEs and a system of two LODEs via two integral transforms


In this paper we prove three theorems to introduce a new method for finding the general solution ( without using any initial conditions ) of the linear ordinary differential equations ( LODEs ) and for the systems of two linear ordinary differential equations with constant coefficients using the integral transform Laplace transform with the aid of the residues and then we prove another two theorems to show that the integral transform Sumudu transform can be used exactly equivalently to Laplace transform in finding the general solutions for these two types of differential equations .