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3y = 0",{"_43":193,"_81":87,"_83":194},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_43":196,"_81":91,"_83":197},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_43":199,"_81":95,"_83":200},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_43":186,"_81":99,"_83":202},"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

",[206],{"_43":207,"_57":208,"_59":209,"_150":151,"_152":210,"_123":211,"_125":211,"_45":212,"_127":209},"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",{"_156":213,"_158":159,"_160":214},4,12302,{"_40":216,"_42":41,"_43":217,"_77":218,"_101":230,"_102":231,"_51":232},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[219,222,225,227],{"_43":220,"_81":82,"_83":221},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_43":223,"_81":87,"_83":224},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_43":216,"_81":91,"_83":226},"

Verdadeiro, falso, verdadeiro

",{"_43":228,"_81":95,"_83":229},"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?

",[206],{"_40":234,"_42":41,"_43":235,"_77":236,"_101":251,"_102":252,"_51":253},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[237,240,243,245,248],{"_43":238,"_81":82,"_83":239},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_43":241,"_81":87,"_83":242},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_43":234,"_81":91,"_83":244},"Indeterminado",{"_43":246,"_81":95,"_83":247},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_43":249,"_81":99,"_83":250},"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????",[206],[206,255,262,272,279,286,287,295,301,306,312,319],{"_43":256,"_57":58,"_59":60,"_150":151,"_152":257,"_123":154,"_125":154,"_45":258,"_127":261},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_156":259,"_158":159,"_160":260},2,11846,"termodinamica-3",{"_43":263,"_57":264,"_59":265,"_150":151,"_152":266,"_123":267,"_125":267,"_45":268,"_127":271},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_156":269,"_158":159,"_160":270},5,30614,"engenharia-mecatronica-1",{"_43":273,"_57":274,"_59":275,"_150":151,"_152":263,"_123":211,"_125":211,"_45":276,"_127":278},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_156":269,"_158":159,"_160":277},25741,"mecanica-3",{"_43":257,"_57":280,"_59":281,"_150":151,"_152":266,"_123":267,"_125":267,"_45":282,"_127":285},"Engenharia Mecânica","engenharia-mecanica",{"_156":283,"_158":159,"_160":284},11,36318,"engenharia-mecanica-2",{"_43":147,"_57":148,"_59":149,"_150":151,"_152":153,"_123":154,"_125":154,"_45":155,"_127":149},{"_43":288,"_57":289,"_59":290,"_150":151,"_152":-5,"_123":291,"_125":291,"_45":292,"_127":290},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_156":293,"_158":159,"_160":294},18,135489,{"_43":296,"_57":58,"_59":60,"_150":151,"_152":207,"_123":297,"_125":297,"_45":298,"_127":300},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_156":159,"_158":159,"_160":299},8597,"termodinamica-5",{"_43":210,"_57":302,"_59":303,"_150":151,"_152":266,"_123":267,"_125":267,"_45":304,"_127":305},"Engenharia de Petróleo","engenharia-de-petroleo",{"_156":269,"_158":159,"_160":214},"engenharia-de-petroleo-1",{"_43":153,"_57":307,"_59":308,"_150":151,"_152":288,"_123":267,"_125":267,"_45":309,"_127":311},"Física","fisica",{"_156":283,"_158":159,"_160":310},13777,"fisica-4",{"_43":266,"_57":313,"_59":314,"_150":151,"_152":-5,"_123":315,"_125":315,"_45":316,"_127":314},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_156":317,"_158":159,"_160":318},29,351586,{"_43":320,"_57":58,"_59":60,"_150":151,"_152":273,"_123":321,"_125":321,"_45":322,"_127":323},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_156":159,"_158":159,"_160":299},"termodinamica-4","tagsTree",[326,330],{"_43":288,"_57":289,"_59":290,"_150":151,"_152":-5,"_123":291,"_125":291,"_45":292,"_127":290,"_162":327},[328],{"_43":153,"_57":307,"_59":308,"_150":151,"_152":288,"_123":267,"_125":267,"_45":309,"_127":311,"_162":329},[146],{"_43":266,"_57":313,"_59":314,"_150":151,"_152":-5,"_123":315,"_125":315,"_45":316,"_127":314,"_162":331},[332,338,342],{"_43":263,"_57":264,"_59":265,"_150":151,"_152":266,"_123":267,"_125":267,"_45":268,"_127":271,"_162":333},[334],{"_43":273,"_57":274,"_59":275,"_150":151,"_152":263,"_123":211,"_125":211,"_45":276,"_127":278,"_162":335},[336],{"_43":320,"_57":58,"_59":60,"_150":151,"_152":273,"_123":321,"_125":321,"_45":322,"_127":323,"_162":337},[],{"_43":257,"_57":280,"_59":281,"_150":151,"_152":266,"_123":267,"_125":267,"_45":282,"_127":285,"_162":339},[340],{"_43":256,"_57":58,"_59":60,"_150":151,"_152":257,"_123":154,"_125":154,"_45":258,"_127":261,"_162":341},[],{"_43":210,"_57":302,"_59":303,"_150":151,"_152":266,"_123":267,"_125":267,"_45":304,"_127":305,"_162":343},[344],{"_43":207,"_57":208,"_59":209,"_150":151,"_152":210,"_123":211,"_125":211,"_45":212,"_127":209,"_162":345},[346],{"_43":296,"_57":58,"_59":60,"_150":151,"_152":207,"_123":297,"_125":297,"_45":298,"_127":300,"_162":347},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários