COMPARISON OF ADOMIAN DECOMPOSITION AND POWER SERIES IN SOLVING SECOND-ORDER LINEAR DIFFERENTIAL EQUATIONS

This paper explores two analytical techniques for obtaining series solutions to second-order linear differential equations with variable coefficients: the Adomian Decomposition Method (ADM) and the Power Series Method (PSM). Both methods offer approximate solutions but differ fundamentally in their approach and computational framework. Through illustrative examples, including cases where all variable coefficients are non-zero, the effectiveness and practical nuances of each method are examined. A comparative analysis highlights their respective advantages and potential limitations in solving complex differential equations. This study aims to provide deeper insight into the applicability of these methods for tackling differential equations with variable coefficients, thereby aiding in the selection of suitable techniques for specific problem classes