(untitled) (THE ACADEMIA, 2025)
In this paper, a new integral transform was applied to solve linear ordinary differential equations with constant co-efficient. Overall, it is a fundamental tool in engineering and applied mathematics, providing a systematic way to analyze and solve dynamic systems and differential equations in a wide range of applications. Integral transforms are an effective tool for evaluating functions, resolving differential equations, and resolving issues in a variety of scientific and technical fields. Integral transform enables us to operate in other domains (such as time, frequency), where the problem’s physical interpretation may be clearer or the mathematical procedures may be simpler. It is a powerful mathematical instrument that solves ordinary differential equations (ODEs) and analyzes linear time-invariant systems, among other things. It is used to investigate several problems in engineering, physics, and applied mathematics. Both ordinary differential equations and a system of linear differential equations with constant coefficients have been solved using this novel transform. Solving linear ordinary differential equations with constant coefficients is the primary use of this method. By taking the Laplace transform of both sides of an ODE, one can convert the differential equation into an algebraic equation, which is often easier to solve.