Mean Square Solutions of Second-Order Random Differential Equations by Using the Differential Transformation Method

The differential transformation method (DTM) is applied to solve second-order random differential equations. In this study, we explore the application of DTM to several examples to demonstrate its effectiveness in obtaining both exact and approximate solutions. The results indicate that DTM provides an efficient and accurate technique for addressing the complexities associated with random differential equations. By transforming the differential equations into algebraic forms, we simplify the computational process, allowing for easier manipulation and solution derivation. This paper highlights the advantages of using DTM in computational mathematics and its potential for solving a broad class of stochastic differential equations.