Comparison of the results obtained by Iman transform with Laplace transform

Many processes in the real world are characterised by principles which are defined in the form of expressions involving rates of change. Mathematically, rates are derivatives and expressions are equations and so we have differential equations. Differential equations play an important role in modelling many problems in scientific fields. Sometimes, the calculations to solve these equations can be very complex and ultimately frustrating. For this reason, many integral transform methods have been proposed by researchers. Because, integral transform methods give consistent solutions to many complex problems and have many application areas such as physics, mechanics, engineering, astronomy. In this work, two integral transforms, the Iman transform and the well-known Laplace transform are studied comparatively to facilitate the solution of linear ordinary differential equations with constant coefficients. Applications of these transforms show that these integral transform methods are closely related to each other.