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3y = 0",{"_43":188,"_81":87,"_83":189},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":191,"_81":91,"_83":192},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":194,"_81":95,"_83":195},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":181,"_81":197,"_83":198},"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

",[202],{"_43":203,"_57":204,"_59":205,"_146":147,"_148":206,"_119":207,"_121":207,"_45":208,"_123":205},"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",{"_152":209,"_154":64,"_155":210},4,12302,{"_40":212,"_42":41,"_43":213,"_77":214,"_97":226,"_98":227,"_51":228},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[215,218,221,223],{"_43":216,"_81":82,"_83":217},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":219,"_81":87,"_83":220},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":212,"_81":91,"_83":222},"

Verdadeiro, falso, verdadeiro

",{"_43":224,"_81":95,"_83":225},"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?

",[202],{"_40":230,"_42":41,"_43":231,"_77":232,"_97":247,"_98":248,"_51":249},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[233,236,239,241,244],{"_43":234,"_81":82,"_83":235},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_43":237,"_81":87,"_83":238},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_43":230,"_81":91,"_83":240},"Indeterminado",{"_43":242,"_81":95,"_83":243},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_43":245,"_81":197,"_83":246},"2e06d948-d37e-4350-afc7-ced04941bcaf","Nenhum","Os polinômios e números fornecidos estão corrompidos (símbolos “????”), impossibilitando aplicar Ruffini e concluir se são raízes. Sem dados completos, o problema é indeterminado.","Emplea la regla de Ruffini para dictaminar si los siguientes números son o no raíces de los polinomios citados:
a) ????3 de ????4????5
b) ????2 de ????2????????2
c) ????1 de 2????????1
d) ????1 de 2????2????",[202],[202,251,258,268,275,282,283,291,297,302,308,315],{"_43":252,"_57":58,"_59":60,"_146":147,"_148":253,"_119":150,"_121":150,"_45":254,"_123":257},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_152":255,"_154":64,"_155":256},2,11846,"termodinamica-3",{"_43":259,"_57":260,"_59":261,"_146":147,"_148":262,"_119":263,"_121":263,"_45":264,"_123":267},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_152":265,"_154":64,"_155":266},5,30614,"engenharia-mecatronica-1",{"_43":269,"_57":270,"_59":271,"_146":147,"_148":259,"_119":207,"_121":207,"_45":272,"_123":274},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_152":265,"_154":64,"_155":273},25741,"mecanica-3",{"_43":253,"_57":276,"_59":277,"_146":147,"_148":262,"_119":263,"_121":263,"_45":278,"_123":281},"Engenharia Mecânica","engenharia-mecanica",{"_152":279,"_154":64,"_155":280},11,36318,"engenharia-mecanica-2",{"_43":143,"_57":144,"_59":145,"_146":147,"_148":149,"_119":150,"_121":150,"_45":151,"_123":145},{"_43":284,"_57":285,"_59":286,"_146":147,"_148":-5,"_119":287,"_121":287,"_45":288,"_123":286},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_152":289,"_154":64,"_155":290},18,135489,{"_43":292,"_57":58,"_59":60,"_146":147,"_148":203,"_119":293,"_121":293,"_45":294,"_123":296},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_152":64,"_154":64,"_155":295},8597,"termodinamica-5",{"_43":206,"_57":298,"_59":299,"_146":147,"_148":262,"_119":263,"_121":263,"_45":300,"_123":301},"Engenharia de Petróleo","engenharia-de-petroleo",{"_152":265,"_154":64,"_155":210},"engenharia-de-petroleo-1",{"_43":149,"_57":303,"_59":304,"_146":147,"_148":284,"_119":263,"_121":263,"_45":305,"_123":307},"Física","fisica",{"_152":279,"_154":64,"_155":306},13777,"fisica-4",{"_43":262,"_57":309,"_59":310,"_146":147,"_148":-5,"_119":311,"_121":311,"_45":312,"_123":310},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_152":313,"_154":64,"_155":314},29,351586,{"_43":316,"_57":58,"_59":60,"_146":147,"_148":269,"_119":317,"_121":317,"_45":318,"_123":319},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_152":64,"_154":64,"_155":295},"termodinamica-4","tagsTree",[322,326],{"_43":284,"_57":285,"_59":286,"_146":147,"_148":-5,"_119":287,"_121":287,"_45":288,"_123":286,"_157":323},[324],{"_43":149,"_57":303,"_59":304,"_146":147,"_148":284,"_119":263,"_121":263,"_45":305,"_123":307,"_157":325},[142],{"_43":262,"_57":309,"_59":310,"_146":147,"_148":-5,"_119":311,"_121":311,"_45":312,"_123":310,"_157":327},[328,334,338],{"_43":259,"_57":260,"_59":261,"_146":147,"_148":262,"_119":263,"_121":263,"_45":264,"_123":267,"_157":329},[330],{"_43":269,"_57":270,"_59":271,"_146":147,"_148":259,"_119":207,"_121":207,"_45":272,"_123":274,"_157":331},[332],{"_43":316,"_57":58,"_59":60,"_146":147,"_148":269,"_119":317,"_121":317,"_45":318,"_123":319,"_157":333},[],{"_43":253,"_57":276,"_59":277,"_146":147,"_148":262,"_119":263,"_121":263,"_45":278,"_123":281,"_157":335},[336],{"_43":252,"_57":58,"_59":60,"_146":147,"_148":253,"_119":150,"_121":150,"_45":254,"_123":257,"_157":337},[],{"_43":206,"_57":298,"_59":299,"_146":147,"_148":262,"_119":263,"_121":263,"_45":300,"_123":301,"_157":339},[340],{"_43":203,"_57":204,"_59":205,"_146":147,"_148":206,"_119":207,"_121":207,"_45":208,"_123":205,"_157":341},[342],{"_43":292,"_57":58,"_59":60,"_146":147,"_148":203,"_119":293,"_121":293,"_45":294,"_123":296,"_157":343},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários