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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

",[188],{"_21":189,"_35":190,"_37":191,"_129":130,"_131":192,"_102":193,"_104":193,"_23":194,"_106":191},"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",{"_135":195,"_137":42,"_138":196},4,12302,{"_18":198,"_20":19,"_21":199,"_56":200,"_80":212,"_81":213,"_29":214},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[201,204,207,209],{"_21":202,"_60":61,"_62":203},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_21":205,"_60":66,"_62":206},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_21":198,"_60":70,"_62":208},"

Verdadeiro, falso, verdadeiro

",{"_21":210,"_60":74,"_62":211},"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?

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a) ????3 de ????4????5
b) ????2 de ????2????????2
c) ????1 de 2????????1
d) ????1 de 2????2????",[238],{"_21":189,"_35":190,"_37":191,"_129":130,"_131":192,"_102":193,"_104":193,"_23":239,"_106":191},{"_135":195,"_137":42,"_138":196},[241,243,250,260,267,274,276,284,290,295,301,308],{"_21":189,"_35":190,"_37":191,"_129":130,"_131":192,"_102":193,"_104":193,"_23":242,"_106":191},{"_135":195,"_137":42,"_138":196},{"_21":244,"_35":36,"_37":38,"_129":130,"_131":245,"_102":133,"_104":133,"_23":246,"_106":249},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_135":247,"_137":42,"_138":248},2,11846,"termodinamica-3",{"_21":251,"_35":252,"_37":253,"_129":130,"_131":254,"_102":255,"_104":255,"_23":256,"_106":259},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_135":257,"_137":42,"_138":258},5,30614,"engenharia-mecatronica-1",{"_21":261,"_35":262,"_37":263,"_129":130,"_131":251,"_102":193,"_104":193,"_23":264,"_106":266},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_135":257,"_137":42,"_138":265},25741,"mecanica-3",{"_21":245,"_35":268,"_37":269,"_129":130,"_131":254,"_102":255,"_104":255,"_23":270,"_106":273},"Engenharia Mecânica","engenharia-mecanica",{"_135":271,"_137":42,"_138":272},11,36318,"engenharia-mecanica-2",{"_21":126,"_35":127,"_37":128,"_129":130,"_131":132,"_102":133,"_104":133,"_23":275,"_106":128},{"_135":136,"_137":42,"_138":139},{"_21":277,"_35":278,"_37":279,"_129":130,"_131":-5,"_102":280,"_104":280,"_23":281,"_106":279},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_135":282,"_137":42,"_138":283},18,135489,{"_21":285,"_35":36,"_37":38,"_129":130,"_131":189,"_102":286,"_104":286,"_23":287,"_106":289},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_135":42,"_137":42,"_138":288},8597,"termodinamica-5",{"_21":192,"_35":291,"_37":292,"_129":130,"_131":254,"_102":255,"_104":255,"_23":293,"_106":294},"Engenharia de Petróleo","engenharia-de-petroleo",{"_135":257,"_137":42,"_138":196},"engenharia-de-petroleo-1",{"_21":132,"_35":296,"_37":297,"_129":130,"_131":277,"_102":255,"_104":255,"_23":298,"_106":300},"Física","fisica",{"_135":271,"_137":42,"_138":299},13777,"fisica-4",{"_21":254,"_35":302,"_37":303,"_129":130,"_131":-5,"_102":304,"_104":304,"_23":305,"_106":303},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_135":306,"_137":42,"_138":307},29,351586,{"_21":309,"_35":36,"_37":38,"_129":130,"_131":261,"_102":310,"_104":310,"_23":311,"_106":312},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_135":42,"_137":42,"_138":288},"termodinamica-4","tagsTree",[315,324],{"_21":277,"_35":278,"_37":279,"_129":130,"_131":-5,"_102":280,"_104":280,"_23":316,"_106":279,"_140":317},{"_135":282,"_137":42,"_138":283},[318],{"_21":132,"_35":296,"_37":297,"_129":130,"_131":277,"_102":255,"_104":255,"_23":319,"_106":300,"_140":320},{"_135":271,"_137":42,"_138":299},[321],{"_21":126,"_35":127,"_37":128,"_129":130,"_131":132,"_102":133,"_104":133,"_23":322,"_106":128,"_140":323},{"_135":136,"_137":42,"_138":139},[],{"_21":254,"_35":302,"_37":303,"_129":130,"_131":-5,"_102":304,"_104":304,"_23":325,"_106":303,"_140":326},{"_135":306,"_137":42,"_138":307},[327,336,342],{"_21":251,"_35":252,"_37":253,"_129":130,"_131":254,"_102":255,"_104":255,"_23":328,"_106":259,"_140":329},{"_135":257,"_137":42,"_138":258},[330],{"_21":261,"_35":262,"_37":263,"_129":130,"_131":251,"_102":193,"_104":193,"_23":331,"_106":266,"_140":332},{"_135":257,"_137":42,"_138":265},[333],{"_21":309,"_35":36,"_37":38,"_129":130,"_131":261,"_102":310,"_104":310,"_23":334,"_106":312,"_140":335},{"_135":42,"_137":42,"_138":288},[],{"_21":245,"_35":268,"_37":269,"_129":130,"_131":254,"_102":255,"_104":255,"_23":337,"_106":273,"_140":338},{"_135":271,"_137":42,"_138":272},[339],{"_21":244,"_35":36,"_37":38,"_129":130,"_131":245,"_102":133,"_104":133,"_23":340,"_106":249,"_140":341},{"_135":247,"_137":42,"_138":248},[],{"_21":192,"_35":291,"_37":292,"_129":130,"_131":254,"_102":255,"_104":255,"_23":343,"_106":294,"_140":344},{"_135":257,"_137":42,"_138":196},[345],{"_21":189,"_35":190,"_37":191,"_129":130,"_131":192,"_102":193,"_104":193,"_23":346,"_106":191,"_140":347},{"_135":195,"_137":42,"_138":196},[348],{"_21":285,"_35":36,"_37":38,"_129":130,"_131":189,"_102":286,"_104":286,"_23":349,"_106":289,"_140":350},{"_135":42,"_137":42,"_138":288},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários