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...M o p u c t a i d e n arficho j appl computat math l journal of doi h fo lanrissn uoj sci applied computational mathematics review article open access method for solving particular solution linear second order ordinary differential equations department aksum university ethiopia abstract in this paper we derive new whenever one their associated homogeneous is given also construct the equation from moreover have general without applying two famous methods undetermined coefficients and variation parameters keywords reduction fundamental set otherwise it non introduction first an that relates unknown with function or more its derivatives respect to dependent variable y independent x defined by variables if depends axy gx only on single such highest derivative appears real world there are physical problems xg thus need solve these axydx v interval satisfies ax identical all where exp dx arbitrary called free solutions which functions f said be linearly expressed solely terms constants expli...