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3y = 0",{"_43":204,"_81":87,"_83":205},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":207,"_81":91,"_83":208},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":210,"_81":95,"_83":211},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":197,"_81":213,"_83":214},"E","y'' - 2y' + 6y = 0","Somente em y''−2y'+6y=0 o polinômio característico r²−2r+6=0 tem Δ<0, gerando raízes complexas conjugadas (1±i√5) e, portanto, solução em termos de exponencial modulando seno e cosseno. Nos demais itens (a–d) o discriminante é ≥0, produzindo raízes reais (distintas ou repetidas).","

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

",[218],{"_43":219,"_57":220,"_59":221,"_146":147,"_148":222,"_119":223,"_121":223,"_45":224,"_123":221},"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",{"_151":225,"_153":64,"_154":226},4,12302,{"_40":228,"_42":41,"_43":229,"_77":230,"_97":242,"_98":243,"_51":244},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[231,234,237,239],{"_43":232,"_81":82,"_83":233},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":235,"_81":87,"_83":236},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":228,"_81":91,"_83":238},"

Verdadeiro, falso, verdadeiro

",{"_43":240,"_81":95,"_83":241},"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????",[218],[218,267,276,282,286,287,288,296,301,309,310,315,321],{"_43":268,"_57":269,"_59":270,"_146":147,"_148":271,"_119":162,"_121":162,"_45":272,"_123":275},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_151":273,"_153":64,"_154":274},5,30614,"engenharia-mecatronica-1",{"_43":277,"_57":58,"_59":60,"_146":147,"_148":278,"_119":279,"_121":279,"_45":280,"_123":281},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_151":64,"_153":64,"_154":172},"resistencia-dos-materiais-6",{"_43":278,"_57":160,"_59":161,"_146":147,"_148":268,"_119":223,"_121":223,"_45":283,"_123":285},{"_151":273,"_153":64,"_154":284},25741,"mecanica-3",{"_43":143,"_57":144,"_59":145,"_146":147,"_148":-5,"_119":149,"_121":149,"_45":150,"_123":145},{"_43":169,"_57":58,"_59":60,"_146":147,"_148":159,"_119":170,"_121":170,"_45":171,"_123":173},{"_43":289,"_57":290,"_59":291,"_146":147,"_148":271,"_119":162,"_121":162,"_45":292,"_123":295},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_151":293,"_153":64,"_154":294},21,45865,"engenharia-civil-3",{"_43":222,"_57":297,"_59":298,"_146":147,"_148":271,"_119":162,"_121":162,"_45":299,"_123":300},"Engenharia de Petróleo","engenharia-de-petroleo",{"_151":273,"_153":64,"_154":226},"engenharia-de-petroleo-1",{"_43":302,"_57":303,"_59":304,"_146":147,"_148":289,"_119":305,"_121":305,"_45":306,"_123":308},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_151":273,"_153":64,"_154":307},8852,"estruturas-1",{"_43":159,"_57":160,"_59":161,"_146":147,"_148":143,"_119":162,"_121":162,"_45":163,"_123":166},{"_43":311,"_57":58,"_59":60,"_146":147,"_148":219,"_119":312,"_121":312,"_45":313,"_123":314},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_151":64,"_153":64,"_154":172},"resistencia-dos-materiais-7",{"_43":316,"_57":317,"_59":60,"_146":147,"_148":302,"_119":318,"_121":318,"_45":319,"_123":320},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_151":64,"_153":64,"_154":172},"resistencia-dos-materiais-5",{"_43":271,"_57":322,"_59":323,"_146":147,"_148":-5,"_119":324,"_121":324,"_45":325,"_123":323},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_151":326,"_153":64,"_154":327},29,351586,"tagsTree",[142,330],{"_43":271,"_57":322,"_59":323,"_146":147,"_148":-5,"_119":324,"_121":324,"_45":325,"_123":323,"_156":331},[332,338,344],{"_43":268,"_57":269,"_59":270,"_146":147,"_148":271,"_119":162,"_121":162,"_45":272,"_123":275,"_156":333},[334],{"_43":278,"_57":160,"_59":161,"_146":147,"_148":268,"_119":223,"_121":223,"_45":283,"_123":285,"_156":335},[336],{"_43":277,"_57":58,"_59":60,"_146":147,"_148":278,"_119":279,"_121":279,"_45":280,"_123":281,"_156":337},[],{"_43":289,"_57":290,"_59":291,"_146":147,"_148":271,"_119":162,"_121":162,"_45":292,"_123":295,"_156":339},[340],{"_43":302,"_57":303,"_59":304,"_146":147,"_148":289,"_119":305,"_121":305,"_45":306,"_123":308,"_156":341},[342],{"_43":316,"_57":317,"_59":60,"_146":147,"_148":302,"_119":318,"_121":318,"_45":319,"_123":320,"_156":343},[],{"_43":222,"_57":297,"_59":298,"_146":147,"_148":271,"_119":162,"_121":162,"_45":299,"_123":300,"_156":345},[346],{"_43":219,"_57":220,"_59":221,"_146":147,"_148":222,"_119":223,"_121":223,"_45":224,"_123":221,"_156":347},[348],{"_43":311,"_57":58,"_59":60,"_146":147,"_148":219,"_119":312,"_121":312,"_45":313,"_123":314,"_156":349},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários