Solutions of Types of Differential Equations: Analytical Method

Abstract

     Differential equations are fundamental in mathematical modeling across various fields such as science, engineering, medicine, economics, astronomy, and environmental science. The theory of differential equations has evolved alongside the sciences where these equations appear, and their solutions are applied. Despite their significance, only a limited number of differential equations have analytical solutions, and even in cases where solutions exist, deriving them can be a complex process. Consequently, numerical methods play a crucial role in solving these equations, as they offer an alternative when analytical solutions are not feasible. This paper discusses the analytical methods for solving various types of differential equations, exploring their applications in diverse real-world problems such as Newton's second law of dynamics, radioactive decay, wave equations, and electrical circuits.