Group classification of second-order delay ordinary differential equations

This research gives a complete Lie group classification of second-order delay ordinary differential equations of the formy″=fx,y,yτ,y′,yτ′,where τ>0τ>0 is the delay, yτ=y(x-τ)andyτ′=y′(x-τ). All classes of second-order delay ordinary differential equations admitting a Lie algebra are presented in the manuscript. The method for finding the solution for this type of differential equation is developed.