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3y = 0",{"_44":192,"_82":88,"_84":193},"6d3c3a1d-8e80-4ff3-b97a-d5b5bca91940","6y'' - y' - y = 0",{"_44":195,"_82":91,"_84":196},"4168ac67-64fd-46ed-a69c-a01dbfcde7ea","y'' - 2y' + y = 0",{"_44":198,"_82":95,"_84":199},"cc7bc8df-6995-4264-ac5a-32ea9b4ed7db","9y'' + 6y' + y = 0",{"_44":185,"_82":99,"_84":201},"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

",[205],{"_44":206,"_58":207,"_60":208,"_150":151,"_152":209,"_123":210,"_125":210,"_46":211,"_127":208},"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":212,"_158":65,"_159":213},4,12302,{"_40":215,"_42":43,"_44":216,"_78":217,"_101":229,"_102":230,"_52":231},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[218,221,224,226],{"_44":219,"_82":83,"_84":220},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_44":222,"_82":88,"_84":223},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_44":215,"_82":91,"_84":225},"

Verdadeiro, falso, verdadeiro

",{"_44":227,"_82":95,"_84":228},"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?

",[205],{"_40":233,"_42":43,"_44":234,"_78":235,"_101":250,"_102":251,"_52":252},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[236,239,242,244,247],{"_44":237,"_82":83,"_84":238},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_44":240,"_82":88,"_84":241},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_44":233,"_82":91,"_84":243},"Indeterminado",{"_44":245,"_82":95,"_84":246},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_44":248,"_82":99,"_84":249},"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????",[205],[205,254,261,271,278,285,286,294,300,305,311,318],{"_44":255,"_58":59,"_60":61,"_150":151,"_152":256,"_123":154,"_125":154,"_46":257,"_127":260},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_156":258,"_158":65,"_159":259},2,11846,"termodinamica-3",{"_44":262,"_58":263,"_60":264,"_150":151,"_152":265,"_123":266,"_125":266,"_46":267,"_127":270},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_156":268,"_158":65,"_159":269},5,30614,"engenharia-mecatronica-1",{"_44":272,"_58":273,"_60":274,"_150":151,"_152":262,"_123":210,"_125":210,"_46":275,"_127":277},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_156":268,"_158":65,"_159":276},25741,"mecanica-3",{"_44":256,"_58":279,"_60":280,"_150":151,"_152":265,"_123":266,"_125":266,"_46":281,"_127":284},"Engenharia Mecânica","engenharia-mecanica",{"_156":282,"_158":65,"_159":283},11,36318,"engenharia-mecanica-2",{"_44":147,"_58":148,"_60":149,"_150":151,"_152":153,"_123":154,"_125":154,"_46":155,"_127":149},{"_44":287,"_58":288,"_60":289,"_150":151,"_152":-5,"_123":290,"_125":290,"_46":291,"_127":289},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_156":292,"_158":65,"_159":293},18,135489,{"_44":295,"_58":59,"_60":61,"_150":151,"_152":206,"_123":296,"_125":296,"_46":297,"_127":299},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_156":65,"_158":65,"_159":298},8597,"termodinamica-5",{"_44":209,"_58":301,"_60":302,"_150":151,"_152":265,"_123":266,"_125":266,"_46":303,"_127":304},"Engenharia de Petróleo","engenharia-de-petroleo",{"_156":268,"_158":65,"_159":213},"engenharia-de-petroleo-1",{"_44":153,"_58":306,"_60":307,"_150":151,"_152":287,"_123":266,"_125":266,"_46":308,"_127":310},"Física","fisica",{"_156":282,"_158":65,"_159":309},13777,"fisica-4",{"_44":265,"_58":312,"_60":313,"_150":151,"_152":-5,"_123":314,"_125":314,"_46":315,"_127":313},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_156":316,"_158":65,"_159":317},29,351586,{"_44":319,"_58":59,"_60":61,"_150":151,"_152":272,"_123":320,"_125":320,"_46":321,"_127":322},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_156":65,"_158":65,"_159":298},"termodinamica-4","tagsTree",[325,329],{"_44":287,"_58":288,"_60":289,"_150":151,"_152":-5,"_123":290,"_125":290,"_46":291,"_127":289,"_161":326},[327],{"_44":153,"_58":306,"_60":307,"_150":151,"_152":287,"_123":266,"_125":266,"_46":308,"_127":310,"_161":328},[146],{"_44":265,"_58":312,"_60":313,"_150":151,"_152":-5,"_123":314,"_125":314,"_46":315,"_127":313,"_161":330},[331,337,341],{"_44":262,"_58":263,"_60":264,"_150":151,"_152":265,"_123":266,"_125":266,"_46":267,"_127":270,"_161":332},[333],{"_44":272,"_58":273,"_60":274,"_150":151,"_152":262,"_123":210,"_125":210,"_46":275,"_127":277,"_161":334},[335],{"_44":319,"_58":59,"_60":61,"_150":151,"_152":272,"_123":320,"_125":320,"_46":321,"_127":322,"_161":336},[],{"_44":256,"_58":279,"_60":280,"_150":151,"_152":265,"_123":266,"_125":266,"_46":281,"_127":284,"_161":338},[339],{"_44":255,"_58":59,"_60":61,"_150":151,"_152":256,"_123":154,"_125":154,"_46":257,"_127":260,"_161":340},[],{"_44":209,"_58":301,"_60":302,"_150":151,"_152":265,"_123":266,"_125":266,"_46":303,"_127":304,"_161":342},[343],{"_44":206,"_58":207,"_60":208,"_150":151,"_152":209,"_123":210,"_125":210,"_46":211,"_127":208,"_161":344},[345],{"_44":295,"_58":59,"_60":61,"_150":151,"_152":206,"_123":296,"_125":296,"_46":297,"_127":299,"_161":346},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários