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

",[208],{"_21":209,"_35":210,"_37":211,"_125":126,"_127":212,"_98":213,"_100":213,"_23":214,"_102":211},"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",{"_130":215,"_132":133,"_134":216},4,12302,{"_18":218,"_20":19,"_21":219,"_56":220,"_76":232,"_77":233,"_29":234},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[221,224,227,229],{"_21":222,"_60":61,"_62":223},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_21":225,"_60":66,"_62":226},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_21":218,"_60":70,"_62":228},"

Verdadeiro, falso, verdadeiro

",{"_21":230,"_60":74,"_62":231},"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????",[258],{"_21":209,"_35":210,"_37":211,"_125":126,"_127":212,"_98":213,"_100":213,"_23":259,"_102":211},{"_130":215,"_132":133,"_134":216},[261,263,272,278,282,284,286,294,299,307,309,314,320],{"_21":209,"_35":210,"_37":211,"_125":126,"_127":212,"_98":213,"_100":213,"_23":262,"_102":211},{"_130":215,"_132":133,"_134":216},{"_21":264,"_35":265,"_37":266,"_125":126,"_127":267,"_98":142,"_100":142,"_23":268,"_102":271},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_130":269,"_132":133,"_134":270},5,30614,"engenharia-mecatronica-1",{"_21":273,"_35":36,"_37":38,"_125":126,"_127":274,"_98":275,"_100":275,"_23":276,"_102":277},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_130":133,"_132":133,"_134":152},"resistencia-dos-materiais-6",{"_21":274,"_35":140,"_37":141,"_125":126,"_127":264,"_98":213,"_100":213,"_23":279,"_102":281},{"_130":269,"_132":133,"_134":280},25741,"mecanica-3",{"_21":122,"_35":123,"_37":124,"_125":126,"_127":-5,"_98":128,"_100":128,"_23":283,"_102":124},{"_130":131,"_132":133,"_134":135},{"_21":149,"_35":36,"_37":38,"_125":126,"_127":139,"_98":150,"_100":150,"_23":285,"_102":153},{"_130":133,"_132":133,"_134":152},{"_21":287,"_35":288,"_37":289,"_125":126,"_127":267,"_98":142,"_100":142,"_23":290,"_102":293},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_130":291,"_132":133,"_134":292},21,45865,"engenharia-civil-3",{"_21":212,"_35":295,"_37":296,"_125":126,"_127":267,"_98":142,"_100":142,"_23":297,"_102":298},"Engenharia de Petróleo","engenharia-de-petroleo",{"_130":269,"_132":133,"_134":216},"engenharia-de-petroleo-1",{"_21":300,"_35":301,"_37":302,"_125":126,"_127":287,"_98":303,"_100":303,"_23":304,"_102":306},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_130":269,"_132":133,"_134":305},8852,"estruturas-1",{"_21":139,"_35":140,"_37":141,"_125":126,"_127":122,"_98":142,"_100":142,"_23":308,"_102":146},{"_130":144,"_132":133,"_134":145},{"_21":310,"_35":36,"_37":38,"_125":126,"_127":209,"_98":311,"_100":311,"_23":312,"_102":313},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_130":133,"_132":133,"_134":152},"resistencia-dos-materiais-7",{"_21":315,"_35":316,"_37":38,"_125":126,"_127":300,"_98":317,"_100":317,"_23":318,"_102":319},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_130":133,"_132":133,"_134":152},"resistencia-dos-materiais-5",{"_21":267,"_35":321,"_37":322,"_125":126,"_127":-5,"_98":323,"_100":323,"_23":324,"_102":322},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_130":325,"_132":133,"_134":326},29,351586,"tagsTree",[329,338],{"_21":122,"_35":123,"_37":124,"_125":126,"_127":-5,"_98":128,"_100":128,"_23":330,"_102":124,"_136":331},{"_130":131,"_132":133,"_134":135},[332],{"_21":139,"_35":140,"_37":141,"_125":126,"_127":122,"_98":142,"_100":142,"_23":333,"_102":146,"_136":334},{"_130":144,"_132":133,"_134":145},[335],{"_21":149,"_35":36,"_37":38,"_125":126,"_127":139,"_98":150,"_100":150,"_23":336,"_102":153,"_136":337},{"_130":133,"_132":133,"_134":152},[],{"_21":267,"_35":321,"_37":322,"_125":126,"_127":-5,"_98":323,"_100":323,"_23":339,"_102":322,"_136":340},{"_130":325,"_132":133,"_134":326},[341,350,359],{"_21":264,"_35":265,"_37":266,"_125":126,"_127":267,"_98":142,"_100":142,"_23":342,"_102":271,"_136":343},{"_130":269,"_132":133,"_134":270},[344],{"_21":274,"_35":140,"_37":141,"_125":126,"_127":264,"_98":213,"_100":213,"_23":345,"_102":281,"_136":346},{"_130":269,"_132":133,"_134":280},[347],{"_21":273,"_35":36,"_37":38,"_125":126,"_127":274,"_98":275,"_100":275,"_23":348,"_102":277,"_136":349},{"_130":133,"_132":133,"_134":152},[],{"_21":287,"_35":288,"_37":289,"_125":126,"_127":267,"_98":142,"_100":142,"_23":351,"_102":293,"_136":352},{"_130":291,"_132":133,"_134":292},[353],{"_21":300,"_35":301,"_37":302,"_125":126,"_127":287,"_98":303,"_100":303,"_23":354,"_102":306,"_136":355},{"_130":269,"_132":133,"_134":305},[356],{"_21":315,"_35":316,"_37":38,"_125":126,"_127":300,"_98":317,"_100":317,"_23":357,"_102":319,"_136":358},{"_130":133,"_132":133,"_134":152},[],{"_21":212,"_35":295,"_37":296,"_125":126,"_127":267,"_98":142,"_100":142,"_23":360,"_102":298,"_136":361},{"_130":269,"_132":133,"_134":216},[362],{"_21":209,"_35":210,"_37":211,"_125":126,"_127":212,"_98":213,"_100":213,"_23":363,"_102":211,"_136":364},{"_130":215,"_132":133,"_134":216},[365],{"_21":310,"_35":36,"_37":38,"_125":126,"_127":209,"_98":311,"_100":311,"_23":366,"_102":313,"_136":367},{"_130":133,"_132":133,"_134":152},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários