Abstract
There is a natural link between contact symmetries (symmetries that leave invariant the first-order contact form) and first integrals of a given second-order ordinary differential equation. It will be shown that the contact symmetry algebra of a general second-order ordinary differential equation is infinite dimensional and it is generated by the functionally independent first integrals of the equation. Moreover, the contact symmetry algebras of second-order equations admitting one, two, three, and eight point symmetries are obtained.
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