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 form y ″ = f x , y , y τ , y ′ , y τ ′ , where τ > 0 is the delay, y τ = y ( x - τ ) and y τ ′ = 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.