المجلة الدولية للعلوم والتقنية

In this research, we presented basic concepts of the differential equation in terms of rank, degree and classification, and to identify the general and specific solutions of these equations, we defined the linear differential equation, we touched on the homogeneous and heterogeneous linear differential equation, and the methods of its solutions using the separation of variables, changing the constants and the integrative factor, and we are applying a mathematical program to solve homogeneous and inhomogeneous linear differential equations of the first order, represent them as mathematical models and use them in the physical properties represented in Newton’s law of cooling (thermal system) and laws of motion (mechanical system), and discussion in the form of curves studying the relationship between time (t) temperature and degree (T).