Solving first order ODE with initial conditions exactly using laplace transform On MATLAB

Abstract

The solution method for first-order ordinary differential equations (ODEs) with constant coefficients and initial conditions is presented in this study and is based on MATLAB. The suggested method depends on Laplace transforms to find exact results. The research introduces a special MATLAB function that is intended to precisely compute the exact solutions of certain ODEs while also offering other details like elapsed time and relevant figures. This method presents a systematic approach to handle these kinds of ODEs, solving the difficulties brought on by constant coefficients and initial conditions. It does this by using Laplace transformations. This method is expected to be used in disciplines like engineering and physics where second-order ODEs are frequent and exact solutions to them are important.