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The quest of developing efficient and accurate classification scheme for solving second order differential equations (DE) with various coefficients to solvable Lie algebra is never ending. We report a novel classification scheme for second order linear delay differential equations (DDEs) of retarded type with constant coefficients to solvable Lie algebra. The absence of an equivalent transformation related with the change in variables is considered to determine the invariant of DDEs in solvable Lie algebra. The infinitesimal generator of DDEs is used to determine the associated symmetry group. The equations are solved and the solvable Lie algebras spanned by these parameters are obtained by satisfying the inclusion property. This method is further extended to classify neutral delay DE and all classes of second order linear DDEs Corresponding author 974 Laheeb Muhsen and Normah Maan with constant coefficients to solvable Lie algebra. The excellent features of the results and successful implementation suggest that our new classifier may constitute a basis for categorizing second order linear DDEs with constant coefficients to solvable Lie Algebra. Mathematics Subject Classification: 34K06 and 17B30

New approach to classify second order linear delay differential equations with constant coefficients to solvable Lie algebra