Abstract

Making use of the formalism of differential forms, it is shown that any second-order ODE, or any system of two first-order ODEs, with differentiable coefficients, can be expressed in the form of the Hamilton equations with the Hamiltonian function being a differentiable function that can be chosen arbitrarily. It is also shown that any nontrivial local one-parameter group of symmetries of a second-order ODE, or a system of two first-order ODEs, is associated with a first integral.

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