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The Lagrangian formalism for variational problem for second-order delayordinary differential equations (DODEs) is developed. The Noether-type operatoridentities and theorems for DODEs of second order are presented. Algebraicconstruction of integrals for DODEs based on symmetries are demonstrated byexamples.

Lagrangian formalism and Noether-type theorems for second-order delay ODEs