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3y = 0",{"_43":195,"_80":86,"_82":196},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":198,"_80":90,"_82":199},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":201,"_80":94,"_82":202},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":188,"_80":98,"_82":204},"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

",[208],{"_43":209,"_56":210,"_58":211,"_149":150,"_151":212,"_122":213,"_124":213,"_45":214,"_126":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",{"_155":215,"_157":158,"_159":216},4,12302,{"_40":218,"_42":41,"_43":219,"_76":220,"_100":232,"_101":233,"_50":234},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[221,224,227,229],{"_43":222,"_80":81,"_82":223},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":225,"_80":86,"_82":226},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":218,"_80":90,"_82":228},"

Verdadeiro, falso, verdadeiro

",{"_43":230,"_80":94,"_82":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],{"_43":209,"_56":210,"_58":211,"_149":150,"_151":212,"_122":213,"_124":213,"_45":259,"_126":211},{"_155":215,"_157":158,"_159":216},[261,263,270,280,287,294,296,304,310,315,321,328],{"_43":209,"_56":210,"_58":211,"_149":150,"_151":212,"_122":213,"_124":213,"_45":262,"_126":211},{"_155":215,"_157":158,"_159":216},{"_43":264,"_56":57,"_58":59,"_149":150,"_151":265,"_122":153,"_124":153,"_45":266,"_126":269},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_155":267,"_157":158,"_159":268},2,11846,"termodinamica-3",{"_43":271,"_56":272,"_58":273,"_149":150,"_151":274,"_122":275,"_124":275,"_45":276,"_126":279},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_155":277,"_157":158,"_159":278},5,30614,"engenharia-mecatronica-1",{"_43":281,"_56":282,"_58":283,"_149":150,"_151":271,"_122":213,"_124":213,"_45":284,"_126":286},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_155":277,"_157":158,"_159":285},25741,"mecanica-3",{"_43":265,"_56":288,"_58":289,"_149":150,"_151":274,"_122":275,"_124":275,"_45":290,"_126":293},"Engenharia Mecânica","engenharia-mecanica",{"_155":291,"_157":158,"_159":292},11,36318,"engenharia-mecanica-2",{"_43":146,"_56":147,"_58":148,"_149":150,"_151":152,"_122":153,"_124":153,"_45":295,"_126":148},{"_155":156,"_157":158,"_159":160},{"_43":297,"_56":298,"_58":299,"_149":150,"_151":-5,"_122":300,"_124":300,"_45":301,"_126":299},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_155":302,"_157":158,"_159":303},18,135489,{"_43":305,"_56":57,"_58":59,"_149":150,"_151":209,"_122":306,"_124":306,"_45":307,"_126":309},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_155":158,"_157":158,"_159":308},8597,"termodinamica-5",{"_43":212,"_56":311,"_58":312,"_149":150,"_151":274,"_122":275,"_124":275,"_45":313,"_126":314},"Engenharia de Petróleo","engenharia-de-petroleo",{"_155":277,"_157":158,"_159":216},"engenharia-de-petroleo-1",{"_43":152,"_56":316,"_58":317,"_149":150,"_151":297,"_122":275,"_124":275,"_45":318,"_126":320},"Física","fisica",{"_155":291,"_157":158,"_159":319},13777,"fisica-4",{"_43":274,"_56":322,"_58":323,"_149":150,"_151":-5,"_122":324,"_124":324,"_45":325,"_126":323},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_155":326,"_157":158,"_159":327},29,351586,{"_43":329,"_56":57,"_58":59,"_149":150,"_151":281,"_122":330,"_124":330,"_45":331,"_126":332},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_155":158,"_157":158,"_159":308},"termodinamica-4","tagsTree",[335,344],{"_43":297,"_56":298,"_58":299,"_149":150,"_151":-5,"_122":300,"_124":300,"_45":336,"_126":299,"_161":337},{"_155":302,"_157":158,"_159":303},[338],{"_43":152,"_56":316,"_58":317,"_149":150,"_151":297,"_122":275,"_124":275,"_45":339,"_126":320,"_161":340},{"_155":291,"_157":158,"_159":319},[341],{"_43":146,"_56":147,"_58":148,"_149":150,"_151":152,"_122":153,"_124":153,"_45":342,"_126":148,"_161":343},{"_155":156,"_157":158,"_159":160},[],{"_43":274,"_56":322,"_58":323,"_149":150,"_151":-5,"_122":324,"_124":324,"_45":345,"_126":323,"_161":346},{"_155":326,"_157":158,"_159":327},[347,356,362],{"_43":271,"_56":272,"_58":273,"_149":150,"_151":274,"_122":275,"_124":275,"_45":348,"_126":279,"_161":349},{"_155":277,"_157":158,"_159":278},[350],{"_43":281,"_56":282,"_58":283,"_149":150,"_151":271,"_122":213,"_124":213,"_45":351,"_126":286,"_161":352},{"_155":277,"_157":158,"_159":285},[353],{"_43":329,"_56":57,"_58":59,"_149":150,"_151":281,"_122":330,"_124":330,"_45":354,"_126":332,"_161":355},{"_155":158,"_157":158,"_159":308},[],{"_43":265,"_56":288,"_58":289,"_149":150,"_151":274,"_122":275,"_124":275,"_45":357,"_126":293,"_161":358},{"_155":291,"_157":158,"_159":292},[359],{"_43":264,"_56":57,"_58":59,"_149":150,"_151":265,"_122":153,"_124":153,"_45":360,"_126":269,"_161":361},{"_155":267,"_157":158,"_159":268},[],{"_43":212,"_56":311,"_58":312,"_149":150,"_151":274,"_122":275,"_124":275,"_45":363,"_126":314,"_161":364},{"_155":277,"_157":158,"_159":216},[365],{"_43":209,"_56":210,"_58":211,"_149":150,"_151":212,"_122":213,"_124":213,"_45":366,"_126":211,"_161":367},{"_155":215,"_157":158,"_159":216},[368],{"_43":305,"_56":57,"_58":59,"_149":150,"_151":209,"_122":306,"_124":306,"_45":369,"_126":309,"_161":370},{"_155":158,"_157":158,"_159":308},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários