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3y = 0",{"_43":204,"_80":86,"_82":205},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":207,"_80":90,"_82":208},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":210,"_80":94,"_82":211},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":197,"_80":213,"_82":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,"_56":220,"_58":221,"_145":146,"_147":222,"_118":223,"_120":223,"_45":224,"_122":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",{"_150":225,"_152":153,"_154":226},4,12302,{"_40":228,"_42":41,"_43":229,"_76":230,"_96":242,"_97":243,"_50":244},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[231,234,237,239],{"_43":232,"_80":81,"_82":233},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":235,"_80":86,"_82":236},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":228,"_80":90,"_82":238},"

Verdadeiro, falso, verdadeiro

",{"_43":240,"_80":94,"_82":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,"_56":269,"_58":270,"_145":146,"_147":271,"_118":162,"_120":162,"_45":272,"_122":275},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_150":273,"_152":153,"_154":274},5,30614,"engenharia-mecatronica-1",{"_43":277,"_56":57,"_58":59,"_145":146,"_147":278,"_118":279,"_120":279,"_45":280,"_122":281},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_150":153,"_152":153,"_154":172},"resistencia-dos-materiais-6",{"_43":278,"_56":160,"_58":161,"_145":146,"_147":268,"_118":223,"_120":223,"_45":283,"_122":285},{"_150":273,"_152":153,"_154":284},25741,"mecanica-3",{"_43":142,"_56":143,"_58":144,"_145":146,"_147":-5,"_118":148,"_120":148,"_45":149,"_122":144},{"_43":169,"_56":57,"_58":59,"_145":146,"_147":159,"_118":170,"_120":170,"_45":171,"_122":173},{"_43":289,"_56":290,"_58":291,"_145":146,"_147":271,"_118":162,"_120":162,"_45":292,"_122":295},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_150":293,"_152":153,"_154":294},21,45865,"engenharia-civil-3",{"_43":222,"_56":297,"_58":298,"_145":146,"_147":271,"_118":162,"_120":162,"_45":299,"_122":300},"Engenharia de Petróleo","engenharia-de-petroleo",{"_150":273,"_152":153,"_154":226},"engenharia-de-petroleo-1",{"_43":302,"_56":303,"_58":304,"_145":146,"_147":289,"_118":305,"_120":305,"_45":306,"_122":308},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_150":273,"_152":153,"_154":307},8852,"estruturas-1",{"_43":159,"_56":160,"_58":161,"_145":146,"_147":142,"_118":162,"_120":162,"_45":163,"_122":166},{"_43":311,"_56":57,"_58":59,"_145":146,"_147":219,"_118":312,"_120":312,"_45":313,"_122":314},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_150":153,"_152":153,"_154":172},"resistencia-dos-materiais-7",{"_43":316,"_56":317,"_58":59,"_145":146,"_147":302,"_118":318,"_120":318,"_45":319,"_122":320},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_150":153,"_152":153,"_154":172},"resistencia-dos-materiais-5",{"_43":271,"_56":322,"_58":323,"_145":146,"_147":-5,"_118":324,"_120":324,"_45":325,"_122":323},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_150":326,"_152":153,"_154":327},29,351586,"tagsTree",[141,330],{"_43":271,"_56":322,"_58":323,"_145":146,"_147":-5,"_118":324,"_120":324,"_45":325,"_122":323,"_156":331},[332,338,344],{"_43":268,"_56":269,"_58":270,"_145":146,"_147":271,"_118":162,"_120":162,"_45":272,"_122":275,"_156":333},[334],{"_43":278,"_56":160,"_58":161,"_145":146,"_147":268,"_118":223,"_120":223,"_45":283,"_122":285,"_156":335},[336],{"_43":277,"_56":57,"_58":59,"_145":146,"_147":278,"_118":279,"_120":279,"_45":280,"_122":281,"_156":337},[],{"_43":289,"_56":290,"_58":291,"_145":146,"_147":271,"_118":162,"_120":162,"_45":292,"_122":295,"_156":339},[340],{"_43":302,"_56":303,"_58":304,"_145":146,"_147":289,"_118":305,"_120":305,"_45":306,"_122":308,"_156":341},[342],{"_43":316,"_56":317,"_58":59,"_145":146,"_147":302,"_118":318,"_120":318,"_45":319,"_122":320,"_156":343},[],{"_43":222,"_56":297,"_58":298,"_145":146,"_147":271,"_118":162,"_120":162,"_45":299,"_122":300,"_156":345},[346],{"_43":219,"_56":220,"_58":221,"_145":146,"_147":222,"_118":223,"_120":223,"_45":224,"_122":221,"_156":347},[348],{"_43":311,"_56":57,"_58":59,"_145":146,"_147":219,"_118":312,"_120":312,"_45":313,"_122":314,"_156":349},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários