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

",[183],{"_21":184,"_35":185,"_37":186,"_125":126,"_127":187,"_98":188,"_100":188,"_23":189,"_102":186},"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",{"_131":190,"_133":134,"_135":191},4,12302,{"_18":193,"_20":19,"_21":194,"_56":195,"_76":207,"_77":208,"_29":209},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[196,199,202,204],{"_21":197,"_60":61,"_62":198},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_21":200,"_60":66,"_62":201},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_21":193,"_60":70,"_62":203},"

Verdadeiro, falso, verdadeiro

",{"_21":205,"_60":74,"_62":206},"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?

",[183],{"_18":211,"_20":19,"_21":212,"_56":213,"_76":228,"_77":229,"_29":230},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[214,217,220,222,225],{"_21":215,"_60":61,"_62":216},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_21":218,"_60":66,"_62":219},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_21":211,"_60":70,"_62":221},"Indeterminado",{"_21":223,"_60":74,"_62":224},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_21":226,"_60":178,"_62":227},"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????",[183],[183,232,239,249,256,263,264,272,278,283,289,296],{"_21":233,"_35":36,"_37":38,"_125":126,"_127":234,"_98":129,"_100":129,"_23":235,"_102":238},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_131":236,"_133":134,"_135":237},2,11846,"termodinamica-3",{"_21":240,"_35":241,"_37":242,"_125":126,"_127":243,"_98":244,"_100":244,"_23":245,"_102":248},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_131":246,"_133":134,"_135":247},5,30614,"engenharia-mecatronica-1",{"_21":250,"_35":251,"_37":252,"_125":126,"_127":240,"_98":188,"_100":188,"_23":253,"_102":255},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_131":246,"_133":134,"_135":254},25741,"mecanica-3",{"_21":234,"_35":257,"_37":258,"_125":126,"_127":243,"_98":244,"_100":244,"_23":259,"_102":262},"Engenharia Mecânica","engenharia-mecanica",{"_131":260,"_133":134,"_135":261},11,36318,"engenharia-mecanica-2",{"_21":122,"_35":123,"_37":124,"_125":126,"_127":128,"_98":129,"_100":129,"_23":130,"_102":124},{"_21":265,"_35":266,"_37":267,"_125":126,"_127":-5,"_98":268,"_100":268,"_23":269,"_102":267},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_131":270,"_133":134,"_135":271},18,135489,{"_21":273,"_35":36,"_37":38,"_125":126,"_127":184,"_98":274,"_100":274,"_23":275,"_102":277},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_131":134,"_133":134,"_135":276},8597,"termodinamica-5",{"_21":187,"_35":279,"_37":280,"_125":126,"_127":243,"_98":244,"_100":244,"_23":281,"_102":282},"Engenharia de Petróleo","engenharia-de-petroleo",{"_131":246,"_133":134,"_135":191},"engenharia-de-petroleo-1",{"_21":128,"_35":284,"_37":285,"_125":126,"_127":265,"_98":244,"_100":244,"_23":286,"_102":288},"Física","fisica",{"_131":260,"_133":134,"_135":287},13777,"fisica-4",{"_21":243,"_35":290,"_37":291,"_125":126,"_127":-5,"_98":292,"_100":292,"_23":293,"_102":291},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_131":294,"_133":134,"_135":295},29,351586,{"_21":297,"_35":36,"_37":38,"_125":126,"_127":250,"_98":298,"_100":298,"_23":299,"_102":300},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_131":134,"_133":134,"_135":276},"termodinamica-4","tagsTree",[303,307],{"_21":265,"_35":266,"_37":267,"_125":126,"_127":-5,"_98":268,"_100":268,"_23":269,"_102":267,"_137":304},[305],{"_21":128,"_35":284,"_37":285,"_125":126,"_127":265,"_98":244,"_100":244,"_23":286,"_102":288,"_137":306},[121],{"_21":243,"_35":290,"_37":291,"_125":126,"_127":-5,"_98":292,"_100":292,"_23":293,"_102":291,"_137":308},[309,315,319],{"_21":240,"_35":241,"_37":242,"_125":126,"_127":243,"_98":244,"_100":244,"_23":245,"_102":248,"_137":310},[311],{"_21":250,"_35":251,"_37":252,"_125":126,"_127":240,"_98":188,"_100":188,"_23":253,"_102":255,"_137":312},[313],{"_21":297,"_35":36,"_37":38,"_125":126,"_127":250,"_98":298,"_100":298,"_23":299,"_102":300,"_137":314},[],{"_21":234,"_35":257,"_37":258,"_125":126,"_127":243,"_98":244,"_100":244,"_23":259,"_102":262,"_137":316},[317],{"_21":233,"_35":36,"_37":38,"_125":126,"_127":234,"_98":129,"_100":129,"_23":235,"_102":238,"_137":318},[],{"_21":187,"_35":279,"_37":280,"_125":126,"_127":243,"_98":244,"_100":244,"_23":281,"_102":282,"_137":320},[321],{"_21":184,"_35":185,"_37":186,"_125":126,"_127":187,"_98":188,"_100":188,"_23":189,"_102":186,"_137":322},[323],{"_21":273,"_35":36,"_37":38,"_125":126,"_127":184,"_98":274,"_100":274,"_23":275,"_102":277,"_137":324},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

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