{"paper":{"title":"A representation formula for solutions of second order ode's with time dependent coefficients and its application to model dissipative oscillations and waves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AP","authors_text":"Richard Kowar","submitted_at":"2019-03-15T13:02:46Z","abstract_excerpt":"In this paper, we model, classify and investigate the solutions of (normalized) second order ode's with \\emph{nonconstant continuous coefficients}. We introduce a generalized \\emph{frequency function} as the solution of a \\emph{nonlinear integro-differential equation}, show its existence and then derive a representation formula for (all) solutions of (normalized) second order ode's with \\emph{nonconstant continuous coefficients}. Because this formula specifies the interplay between the coefficients of the ode, the \\emph{relaxation function} (\"strongly\" decreasing positive function) and the fre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.06510","kind":"arxiv","version":2},"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"}