On the Application of the Emad-Sara Transform Technique to the Solution of Complex Differential Equations

Abstract

When attempting to express a differential equation of the first order, it is usual practice to use the equation represented by dy/dx= f(x,y). The above equation contains a function denoted by the notation embodied by f(x,y), defined on a portion of the xy-plane and dependent on two variables, x, and y, which are independent variables. The equation considered to be of the first order is the one that has just the first derivative, which is denoted by the notation dy/dx since there are no higher-order derivatives present in the equation. It is usual practice to make use of the differential equation when attempting to explain the connection that exists between a function and the derivatives of that function. Using this technique to identify functions inside a given domain in physics, chemistry, and many other fields of science is feasible. In order to do so, it is necessary to have previous knowledge about functions and the derivatives of those functions. In this article, the Emad-Sara transformation is presented as a method for identifying the general solution of complex differential equations of the first order that have constant coefficients. This transformation may be used to get the general solution of these equations. This approach, which is both practical and economical, may be used to find solutions to a wide variety of linear operator equations. These equations can range from simple to complex