{"paper":{"title":"Integrability cases for the anharmonic oscillator equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Francisco S. N. Lobo, M. K. Mak, Tiberiu Harko","submitted_at":"2013-04-03T12:54:03Z","abstract_excerpt":"Using N. Euler's theorem on the integrability of the general anharmonic oscillator equation \\cite{12}, we present three distinct classes of general solutions of the highly nonlinear second order ordinary differential equation $\\frac{d^{2}x}{dt^{2}}+f_{1}\\left(t\\right) \\frac{dx}{dt}+f_{2}\\left(t\\right) x+f_{3}\\left(t\\right) x^{n}=0$. The first exact solution is obtained from a particular solution of the point transformed equation $d^{2}X/dT^{2}+X^{n}\\left(T\\right) =0$, $n\\notin \\left\\{-3,-1,0,1\\right\\} $, which is equivalent to the anharmonic oscillator equation if the coefficients $f_{i}(t)$, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1468","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}