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3y = 0",{"_43":202,"_89":95,"_91":203},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":205,"_89":206,"_91":207},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","C","y'' - 2y' + y = 0",{"_43":209,"_89":210,"_91":211},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","D","9y'' + 6y' + y = 0",{"_43":195,"_89":213,"_91":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":161,"_121":161,"_45":223,"_123":226},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_151":224,"_153":154,"_155":225},5,30614,"engenharia-mecatronica-1",{"_40":228,"_42":41,"_43":229,"_85":230,"_97":242,"_98":243,"_51":244},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[231,234,237,239],{"_43":232,"_89":90,"_91":233},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":235,"_89":95,"_91":236},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":228,"_89":206,"_91":238},"

Verdadeiro, falso, verdadeiro

",{"_43":240,"_89":210,"_91":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????",[268],{"_43":219,"_57":220,"_59":221,"_146":147,"_148":222,"_119":161,"_121":161,"_45":269,"_123":226},{"_151":224,"_153":154,"_155":225},[271,273,279,281,283],{"_43":219,"_57":220,"_59":221,"_146":147,"_148":222,"_119":161,"_121":161,"_45":272,"_123":226},{"_151":224,"_153":154,"_155":225},{"_43":274,"_57":58,"_59":60,"_146":147,"_148":219,"_119":275,"_121":275,"_45":276,"_123":278},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T03:44:35.328997+00:00",{"_151":224,"_153":154,"_155":277},25741,"mecanica-3",{"_43":143,"_57":144,"_59":145,"_146":147,"_148":-5,"_119":149,"_121":149,"_45":280,"_123":145},{"_151":152,"_153":154,"_155":156},{"_43":160,"_57":58,"_59":60,"_146":147,"_148":143,"_119":161,"_121":161,"_45":282,"_123":165},{"_151":163,"_153":154,"_155":164},{"_43":222,"_57":284,"_59":285,"_146":147,"_148":-5,"_119":286,"_121":286,"_45":287,"_123":285},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_151":288,"_153":154,"_155":289},29,351586,"tagsTree",[292,298],{"_43":143,"_57":144,"_59":145,"_146":147,"_148":-5,"_119":149,"_121":149,"_45":293,"_123":145,"_157":294},{"_151":152,"_153":154,"_155":156},[295],{"_43":160,"_57":58,"_59":60,"_146":147,"_148":143,"_119":161,"_121":161,"_45":296,"_123":165,"_157":297},{"_151":163,"_153":154,"_155":164},[],{"_43":222,"_57":284,"_59":285,"_146":147,"_148":-5,"_119":286,"_121":286,"_45":299,"_123":285,"_157":300},{"_151":288,"_153":154,"_155":289},[301],{"_43":219,"_57":220,"_59":221,"_146":147,"_148":222,"_119":161,"_121":161,"_45":302,"_123":226,"_157":303},{"_151":224,"_153":154,"_155":225},[304],{"_43":274,"_57":58,"_59":60,"_146":147,"_148":219,"_119":275,"_121":275,"_45":305,"_123":278,"_157":306},{"_151":224,"_153":154,"_155":277},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários