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3y = 0",{"_43":209,"_81":87,"_83":210},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":212,"_81":91,"_83":213},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":215,"_81":95,"_83":216},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":202,"_81":99,"_83":218},"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

",[222],{"_43":223,"_57":224,"_59":225,"_150":151,"_152":226,"_123":227,"_125":227,"_45":228,"_127":225},"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",{"_155":229,"_157":158,"_159":230},4,12302,{"_40":232,"_42":41,"_43":233,"_77":234,"_101":246,"_102":247,"_51":248},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[235,238,241,243],{"_43":236,"_81":82,"_83":237},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":239,"_81":87,"_83":240},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":232,"_81":91,"_83":242},"

Verdadeiro, falso, verdadeiro

",{"_43":244,"_81":95,"_83":245},"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????",[222],[222,271,280,286,290,291,292,300,305,313,314,319,325],{"_43":272,"_57":273,"_59":274,"_150":151,"_152":275,"_123":167,"_125":167,"_45":276,"_127":279},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_155":277,"_157":158,"_159":278},5,30614,"engenharia-mecatronica-1",{"_43":281,"_57":58,"_59":60,"_150":151,"_152":282,"_123":283,"_125":283,"_45":284,"_127":285},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_155":158,"_157":158,"_159":177},"resistencia-dos-materiais-6",{"_43":282,"_57":165,"_59":166,"_150":151,"_152":272,"_123":227,"_125":227,"_45":287,"_127":289},{"_155":277,"_157":158,"_159":288},25741,"mecanica-3",{"_43":147,"_57":148,"_59":149,"_150":151,"_152":-5,"_123":153,"_125":153,"_45":154,"_127":149},{"_43":174,"_57":58,"_59":60,"_150":151,"_152":164,"_123":175,"_125":175,"_45":176,"_127":178},{"_43":293,"_57":294,"_59":295,"_150":151,"_152":275,"_123":167,"_125":167,"_45":296,"_127":299},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_155":297,"_157":158,"_159":298},21,45865,"engenharia-civil-3",{"_43":226,"_57":301,"_59":302,"_150":151,"_152":275,"_123":167,"_125":167,"_45":303,"_127":304},"Engenharia de Petróleo","engenharia-de-petroleo",{"_155":277,"_157":158,"_159":230},"engenharia-de-petroleo-1",{"_43":306,"_57":307,"_59":308,"_150":151,"_152":293,"_123":309,"_125":309,"_45":310,"_127":312},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_155":277,"_157":158,"_159":311},8852,"estruturas-1",{"_43":164,"_57":165,"_59":166,"_150":151,"_152":147,"_123":167,"_125":167,"_45":168,"_127":171},{"_43":315,"_57":58,"_59":60,"_150":151,"_152":223,"_123":316,"_125":316,"_45":317,"_127":318},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_155":158,"_157":158,"_159":177},"resistencia-dos-materiais-7",{"_43":320,"_57":321,"_59":60,"_150":151,"_152":306,"_123":322,"_125":322,"_45":323,"_127":324},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_155":158,"_157":158,"_159":177},"resistencia-dos-materiais-5",{"_43":275,"_57":326,"_59":327,"_150":151,"_152":-5,"_123":328,"_125":328,"_45":329,"_127":327},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_155":330,"_157":158,"_159":331},29,351586,"tagsTree",[146,334],{"_43":275,"_57":326,"_59":327,"_150":151,"_152":-5,"_123":328,"_125":328,"_45":329,"_127":327,"_161":335},[336,342,348],{"_43":272,"_57":273,"_59":274,"_150":151,"_152":275,"_123":167,"_125":167,"_45":276,"_127":279,"_161":337},[338],{"_43":282,"_57":165,"_59":166,"_150":151,"_152":272,"_123":227,"_125":227,"_45":287,"_127":289,"_161":339},[340],{"_43":281,"_57":58,"_59":60,"_150":151,"_152":282,"_123":283,"_125":283,"_45":284,"_127":285,"_161":341},[],{"_43":293,"_57":294,"_59":295,"_150":151,"_152":275,"_123":167,"_125":167,"_45":296,"_127":299,"_161":343},[344],{"_43":306,"_57":307,"_59":308,"_150":151,"_152":293,"_123":309,"_125":309,"_45":310,"_127":312,"_161":345},[346],{"_43":320,"_57":321,"_59":60,"_150":151,"_152":306,"_123":322,"_125":322,"_45":323,"_127":324,"_161":347},[],{"_43":226,"_57":301,"_59":302,"_150":151,"_152":275,"_123":167,"_125":167,"_45":303,"_127":304,"_161":349},[350],{"_43":223,"_57":224,"_59":225,"_150":151,"_152":226,"_123":227,"_125":227,"_45":228,"_127":225,"_161":351},[352],{"_43":315,"_57":58,"_59":60,"_150":151,"_152":223,"_123":316,"_125":316,"_45":317,"_127":318,"_161":353},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários