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González Gascón, Francisco Ramos, F.B. Aguirre Dabán, Eduardo 2023-06-21T02:04:39Z 2023-06-21T02:04:39Z 1982 1089-7658 http://0-link.aip.org.cisne.sim.ucm.es/link/doi/10.1063/1.525306 https://hdl.handle.net/20.500.14352/64795 http://0-link.aip.org.cisne.sim.ucm.es/link/doi/10.1063/1.525306 http://aip.org/ It is shown that any first integral of type P2()—a polynomial of degree 2 in —of the differential equation =Vx can be obtained from a pointlike gauge symmetry of the action AL associated to L= 1/2 2+V(t,x). The same result holds for any first integral of kind Pn() when dynamical symmetries of AL polynomials in are allowed. The neccessary and sufficient conditions that V(t,x) must satisfy in order that =Vx possesses a first integral of type Pn() have been obtained. These conditions reduce (when n=2) to a condition obtained by Leach. The computational advantages and difficulties which appear in order to obtain first integrals for type Pn() are also briefly discussed metadata only access On the polynomial first integrals of certain second‐order differential equations journal article