Abstract
In this paper, we consider a general anharmonic oscillator of the form \(\ddot x + {f_1}(t)\dot x + {f_2}(t)x + {f_3}(t){x^n} = 0\), with n ∈ Q. We seek the most general conditions on the functions f1, ƒ2 and ƒ3, by which the equation may be integrable, as well as conditions for the existence of Lie point symmetries. Time-dependent first integrals are constructed. A nonpoint transformation is introduced by which the equation is linearized.
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Euler, N. Transformation Properties of \(\ddot x + {f_1}(t)\dot x + {f_2}(t)x + {f_3}(t){x^n} = 0\). J Nonlinear Math Phys 4, 310–337 (1997). https://doi.org/10.2991/jnmp.1997.4.3-4.7
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DOI: https://doi.org/10.2991/jnmp.1997.4.3-4.7