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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

",[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

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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????",[183],[183,232,238,248,255,262,263,271,277,282,288,295],{"_21":233,"_35":36,"_37":38,"_125":126,"_127":234,"_98":129,"_100":129,"_23":235,"_102":237},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_131":42,"_133":134,"_135":236},11846,"termodinamica-3",{"_21":239,"_35":240,"_37":241,"_125":126,"_127":242,"_98":243,"_100":243,"_23":244,"_102":247},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_131":245,"_133":134,"_135":246},5,30614,"engenharia-mecatronica-1",{"_21":249,"_35":250,"_37":251,"_125":126,"_127":239,"_98":188,"_100":188,"_23":252,"_102":254},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_131":245,"_133":134,"_135":253},25741,"mecanica-3",{"_21":234,"_35":256,"_37":257,"_125":126,"_127":242,"_98":243,"_100":243,"_23":258,"_102":261},"Engenharia Mecânica","engenharia-mecanica",{"_131":259,"_133":134,"_135":260},11,36318,"engenharia-mecanica-2",{"_21":122,"_35":123,"_37":124,"_125":126,"_127":128,"_98":129,"_100":129,"_23":130,"_102":124},{"_21":264,"_35":265,"_37":266,"_125":126,"_127":-5,"_98":267,"_100":267,"_23":268,"_102":266},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_131":269,"_133":134,"_135":270},18,135489,{"_21":272,"_35":36,"_37":38,"_125":126,"_127":184,"_98":273,"_100":273,"_23":274,"_102":276},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_131":134,"_133":134,"_135":275},8597,"termodinamica-5",{"_21":187,"_35":278,"_37":279,"_125":126,"_127":242,"_98":243,"_100":243,"_23":280,"_102":281},"Engenharia de Petróleo","engenharia-de-petroleo",{"_131":245,"_133":134,"_135":191},"engenharia-de-petroleo-1",{"_21":128,"_35":283,"_37":284,"_125":126,"_127":264,"_98":243,"_100":243,"_23":285,"_102":287},"Física","fisica",{"_131":259,"_133":134,"_135":286},13777,"fisica-4",{"_21":242,"_35":289,"_37":290,"_125":126,"_127":-5,"_98":291,"_100":291,"_23":292,"_102":290},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_131":293,"_133":134,"_135":294},29,351586,{"_21":296,"_35":36,"_37":38,"_125":126,"_127":249,"_98":297,"_100":297,"_23":298,"_102":299},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_131":134,"_133":134,"_135":275},"termodinamica-4","tagsTree",[302,306],{"_21":264,"_35":265,"_37":266,"_125":126,"_127":-5,"_98":267,"_100":267,"_23":268,"_102":266,"_137":303},[304],{"_21":128,"_35":283,"_37":284,"_125":126,"_127":264,"_98":243,"_100":243,"_23":285,"_102":287,"_137":305},[121],{"_21":242,"_35":289,"_37":290,"_125":126,"_127":-5,"_98":291,"_100":291,"_23":292,"_102":290,"_137":307},[308,314,318],{"_21":239,"_35":240,"_37":241,"_125":126,"_127":242,"_98":243,"_100":243,"_23":244,"_102":247,"_137":309},[310],{"_21":249,"_35":250,"_37":251,"_125":126,"_127":239,"_98":188,"_100":188,"_23":252,"_102":254,"_137":311},[312],{"_21":296,"_35":36,"_37":38,"_125":126,"_127":249,"_98":297,"_100":297,"_23":298,"_102":299,"_137":313},[],{"_21":234,"_35":256,"_37":257,"_125":126,"_127":242,"_98":243,"_100":243,"_23":258,"_102":261,"_137":315},[316],{"_21":233,"_35":36,"_37":38,"_125":126,"_127":234,"_98":129,"_100":129,"_23":235,"_102":237,"_137":317},[],{"_21":187,"_35":278,"_37":279,"_125":126,"_127":242,"_98":243,"_100":243,"_23":280,"_102":281,"_137":319},[320],{"_21":184,"_35":185,"_37":186,"_125":126,"_127":187,"_98":188,"_100":188,"_23":189,"_102":186,"_137":321},[322],{"_21":272,"_35":36,"_37":38,"_125":126,"_127":184,"_98":273,"_100":273,"_23":274,"_102":276,"_137":323},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários