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The solutions are obtained by transforming the equation Li\\'{e}nard equation to an equivalent first kind first order Abel type equation given by $\\frac{dv}{dy} =f\\left( y\\right) v^{3-n}+k\\left( y\\right) v^{3-m}+g\\left( y\\right) v^{2}+h\\left( y\\right) "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1908.03730","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-08-10T11:00:22Z","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"title_canon_sha256":"bfab0954848fa2ca48fec34960531f19b80859c5a80b915a7ec5a409a43c5a85","abstract_canon_sha256":"b072d21428fd2764561ee68e0a51da572f1fdf8ab7c7674cfb7afbf0fb96bd80"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:03:19.919755Z","signature_b64":"lVuHap04CcH7V0iwFGSIWMm2WeyR4ujvM/eGGzwqc+nJYYXx4r+3NMkDhR5NlxcJu7tNdnAb8nh2OfxyrT5eBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c85a9e8caa959f7faf9291f1439ebf5e75e227220f3a189926d97e288799a484","last_reissued_at":"2026-07-05T01:03:19.919308Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:03:19.919308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the integrability of the Abel and of the extended Li\\'{e}nard equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.SI"],"primary_cat":"math.CA","authors_text":"Man Kwong Mak, Tiberiu Harko","submitted_at":"2019-08-10T11:00:22Z","abstract_excerpt":"We present some exact integrability cases of the extended Li\\'{e}nard equation $y^{\\prime \\prime }+f\\left( y\\right) \\left(y^{\\prime }\\right)^{n}+k\\left( y\\right) \\left(y^{\\prime }\\right)^{m}+g\\left(y\\right) y^{\\prime }+h\\left( y\\right) =0$, with $n>0$ and $m>0$ arbitrary constants, while $f(y)$, $k(y)$, $g(y)$, and $h(y)$ are arbitrary functions. 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