Classification of Second Order Functional Differential Equations with Constant Coefficients to Solvable Lie Algebras

In this paper, we shall apply symmetry analysis to second order functional differential equations with constant coefficients. The determining equations of the admitted Lie group are constructed in a manner different from that of the existing literature for delay differential equations. We define the standard Lie bracket and make a complete classification of the second order linear functional differential equations with constant coefficients, to solvable Lie algebras. We also classify some second order non-linear functional differential equations with constant coefficients, to solvable Lie algebras.