Resolva as seguintes EDOs determinando a solução geral e, quando houver condições iniciais do PVI, a solução particular.

(a) y'' + 2y' - 3y = 0

(b) 6y'' - y' - y = 0

(d) 9y'' + 6y' + y = 0

(e) y'' - 2y' + 6y = 0

(f) 4y'' + 9y = 0

(g) 6y'' - 5y' + y = 0; \\, y(0) = 4; \\, y'(0) = 0

(h) y'' + 4y' + 4y = 0; \\, y(-1) = 2; \\, y'(-1) = 1

(i) y'' + y = 0; \\, y\bigg(\\frac{\\pi}{3}\\bigg) = 2; \\, y'\\bigg(\\frac{\\pi}{3}\\bigg) = -4

(j) y'' - 2y' - 3y = 3e^{2t}

(k) y'' + 9y = t^2 e^{3t} + 6

(l) 2y'' + 3y' + y = t^2 + 3 \\sin(t)

(m) y'' + y' - 2y = 2t; \\, y(0) = 0; \\, y'(0) = 1

(n) y'' - 2y' + y = te^t + 4; \\, y(0) = 1; \\, y'(0) = 1

(o) y'' + 4y = 3 \\sin(2t); \\, y(0) = 2; \\, y'(0) = -1

",[196],{"_21":197,"_32":198,"_34":199,"_139":140,"_141":200,"_112":201,"_114":201,"_23":202,"_116":199},"6516bbbd-f2a3-4710-8382-702240b17836","Mecânica na Engenharia de Petróleo","mecanica-na-engenharia-de-petroleo","b787e438-0ab3-454c-ab43-5d3d14c2720d","2025-04-29T03:44:35.328997+00:00",{"_145":203,"_147":148,"_149":204},4,12302,{"_18":206,"_20":19,"_21":207,"_66":208,"_90":220,"_91":221,"_28":222},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[209,212,215,217],{"_21":210,"_70":71,"_72":211},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_21":213,"_70":76,"_72":214},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_21":206,"_70":80,"_72":216},"

Verdadeiro, falso, verdadeiro

",{"_21":218,"_70":84,"_72":219},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","85,5 % decomposto → 14,5 % restante.\nN/N0 = 0,145 ⇒ t = ln(1/0,145)/(ln2/5730) ≈ 1,6×10⁴ anos.\nItens prováveis: (1) resta 14,5 % do C-14 (V); (2) idade ≈ 1,2×10⁴ anos ou 3 meias-vidas (F); (3) t½ do C-14 = 5730 anos (V). Sequência: V-F-V, correspondendo à alternativa c.","

Qual é a idade da madeira na qual 85,5\\% do C-14 se decompos?

",[196],{"_18":224,"_20":19,"_21":225,"_66":226,"_90":241,"_91":242,"_28":243},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[227,230,233,235,238],{"_21":228,"_70":71,"_72":229},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_21":231,"_70":76,"_72":232},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_21":224,"_70":80,"_72":234},"Indeterminado",{"_21":236,"_70":84,"_72":237},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_21":239,"_70":88,"_72":240},"2e06d948-d37e-4350-afc7-ced04941bcaf","Nenhum","Os polinômios e números fornecidos estão corrompidos (símbolos “????”), impossibilitando aplicar Ruffini e concluir se são raízes. Sem dados completos, o problema é indeterminado.","Emplea la regla de Ruffini para dictaminar si los siguientes números son o no raíces de los polinomios citados:
a) ????3 de ????4????5
b) ????2 de ????2????????2
c) ????1 de 2????????1
d) ????1 de 2????2????",[196],[196,245,252,262,269,276,277,285,291,296,302,309],{"_21":246,"_32":47,"_34":48,"_139":140,"_141":247,"_112":143,"_114":143,"_23":248,"_116":251},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_145":249,"_147":148,"_149":250},2,11846,"termodinamica-3",{"_21":253,"_32":254,"_34":255,"_139":140,"_141":256,"_112":257,"_114":257,"_23":258,"_116":261},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_145":259,"_147":148,"_149":260},5,30614,"engenharia-mecatronica-1",{"_21":263,"_32":264,"_34":265,"_139":140,"_141":253,"_112":201,"_114":201,"_23":266,"_116":268},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_145":259,"_147":148,"_149":267},25741,"mecanica-3",{"_21":247,"_32":270,"_34":271,"_139":140,"_141":256,"_112":257,"_114":257,"_23":272,"_116":275},"Engenharia Mecânica","engenharia-mecanica",{"_145":273,"_147":148,"_149":274},11,36318,"engenharia-mecanica-2",{"_21":136,"_32":137,"_34":138,"_139":140,"_141":142,"_112":143,"_114":143,"_23":144,"_116":138},{"_21":278,"_32":279,"_34":280,"_139":140,"_141":-5,"_112":281,"_114":281,"_23":282,"_116":280},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_145":283,"_147":148,"_149":284},18,135489,{"_21":286,"_32":47,"_34":48,"_139":140,"_141":197,"_112":287,"_114":287,"_23":288,"_116":290},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_145":148,"_147":148,"_149":289},8597,"termodinamica-5",{"_21":200,"_32":292,"_34":293,"_139":140,"_141":256,"_112":257,"_114":257,"_23":294,"_116":295},"Engenharia de Petróleo","engenharia-de-petroleo",{"_145":259,"_147":148,"_149":204},"engenharia-de-petroleo-1",{"_21":142,"_32":297,"_34":298,"_139":140,"_141":278,"_112":257,"_114":257,"_23":299,"_116":301},"Física","fisica",{"_145":273,"_147":148,"_149":300},13777,"fisica-4",{"_21":256,"_32":303,"_34":304,"_139":140,"_141":-5,"_112":305,"_114":305,"_23":306,"_116":304},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_145":307,"_147":148,"_149":308},29,351586,{"_21":310,"_32":47,"_34":48,"_139":140,"_141":263,"_112":311,"_114":311,"_23":312,"_116":313},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_145":148,"_147":148,"_149":289},"termodinamica-4","tagsTree",[316,320],{"_21":278,"_32":279,"_34":280,"_139":140,"_141":-5,"_112":281,"_114":281,"_23":282,"_116":280,"_151":317},[318],{"_21":142,"_32":297,"_34":298,"_139":140,"_141":278,"_112":257,"_114":257,"_23":299,"_116":301,"_151":319},[135],{"_21":256,"_32":303,"_34":304,"_139":140,"_141":-5,"_112":305,"_114":305,"_23":306,"_116":304,"_151":321},[322,328,332],{"_21":253,"_32":254,"_34":255,"_139":140,"_141":256,"_112":257,"_114":257,"_23":258,"_116":261,"_151":323},[324],{"_21":263,"_32":264,"_34":265,"_139":140,"_141":253,"_112":201,"_114":201,"_23":266,"_116":268,"_151":325},[326],{"_21":310,"_32":47,"_34":48,"_139":140,"_141":263,"_112":311,"_114":311,"_23":312,"_116":313,"_151":327},[],{"_21":247,"_32":270,"_34":271,"_139":140,"_141":256,"_112":257,"_114":257,"_23":272,"_116":275,"_151":329},[330],{"_21":246,"_32":47,"_34":48,"_139":140,"_141":247,"_112":143,"_114":143,"_23":248,"_116":251,"_151":331},[],{"_21":200,"_32":292,"_34":293,"_139":140,"_141":256,"_112":257,"_114":257,"_23":294,"_116":295,"_151":333},[334],{"_21":197,"_32":198,"_34":199,"_139":140,"_141":200,"_112":201,"_114":201,"_23":202,"_116":199,"_151":335},[336],{"_21":286,"_32":47,"_34":48,"_139":140,"_141":197,"_112":287,"_114":287,"_23":288,"_116":290,"_151":337},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

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