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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

",[185],{"_21":186,"_35":187,"_37":188,"_129":130,"_131":189,"_102":190,"_104":190,"_23":191,"_106":188},"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",{"_135":192,"_137":42,"_138":193},4,12302,{"_18":195,"_20":19,"_21":196,"_56":197,"_80":209,"_81":210,"_29":211},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[198,201,204,206],{"_21":199,"_60":61,"_62":200},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_21":202,"_60":66,"_62":203},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_21":195,"_60":70,"_62":205},"

Verdadeiro, falso, verdadeiro

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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?

",[185],{"_18":213,"_20":19,"_21":214,"_56":215,"_80":230,"_81":231,"_29":232},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[216,219,222,224,227],{"_21":217,"_60":61,"_62":218},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_21":220,"_60":66,"_62":221},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_21":213,"_60":70,"_62":223},"Indeterminado",{"_21":225,"_60":74,"_62":226},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_21":228,"_60":78,"_62":229},"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????",[185],[185,234,241,251,258,265,266,274,280,285,291,298],{"_21":235,"_35":36,"_37":38,"_129":130,"_131":236,"_102":133,"_104":133,"_23":237,"_106":240},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_135":238,"_137":42,"_138":239},2,11846,"termodinamica-3",{"_21":242,"_35":243,"_37":244,"_129":130,"_131":245,"_102":246,"_104":246,"_23":247,"_106":250},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_135":248,"_137":42,"_138":249},5,30614,"engenharia-mecatronica-1",{"_21":252,"_35":253,"_37":254,"_129":130,"_131":242,"_102":190,"_104":190,"_23":255,"_106":257},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_135":248,"_137":42,"_138":256},25741,"mecanica-3",{"_21":236,"_35":259,"_37":260,"_129":130,"_131":245,"_102":246,"_104":246,"_23":261,"_106":264},"Engenharia Mecânica","engenharia-mecanica",{"_135":262,"_137":42,"_138":263},11,36318,"engenharia-mecanica-2",{"_21":126,"_35":127,"_37":128,"_129":130,"_131":132,"_102":133,"_104":133,"_23":134,"_106":128},{"_21":267,"_35":268,"_37":269,"_129":130,"_131":-5,"_102":270,"_104":270,"_23":271,"_106":269},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_135":272,"_137":42,"_138":273},18,135489,{"_21":275,"_35":36,"_37":38,"_129":130,"_131":186,"_102":276,"_104":276,"_23":277,"_106":279},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_135":42,"_137":42,"_138":278},8597,"termodinamica-5",{"_21":189,"_35":281,"_37":282,"_129":130,"_131":245,"_102":246,"_104":246,"_23":283,"_106":284},"Engenharia de Petróleo","engenharia-de-petroleo",{"_135":248,"_137":42,"_138":193},"engenharia-de-petroleo-1",{"_21":132,"_35":286,"_37":287,"_129":130,"_131":267,"_102":246,"_104":246,"_23":288,"_106":290},"Física","fisica",{"_135":262,"_137":42,"_138":289},13777,"fisica-4",{"_21":245,"_35":292,"_37":293,"_129":130,"_131":-5,"_102":294,"_104":294,"_23":295,"_106":293},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_135":296,"_137":42,"_138":297},29,351586,{"_21":299,"_35":36,"_37":38,"_129":130,"_131":252,"_102":300,"_104":300,"_23":301,"_106":302},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_135":42,"_137":42,"_138":278},"termodinamica-4","tagsTree",[305,309],{"_21":267,"_35":268,"_37":269,"_129":130,"_131":-5,"_102":270,"_104":270,"_23":271,"_106":269,"_140":306},[307],{"_21":132,"_35":286,"_37":287,"_129":130,"_131":267,"_102":246,"_104":246,"_23":288,"_106":290,"_140":308},[125],{"_21":245,"_35":292,"_37":293,"_129":130,"_131":-5,"_102":294,"_104":294,"_23":295,"_106":293,"_140":310},[311,317,321],{"_21":242,"_35":243,"_37":244,"_129":130,"_131":245,"_102":246,"_104":246,"_23":247,"_106":250,"_140":312},[313],{"_21":252,"_35":253,"_37":254,"_129":130,"_131":242,"_102":190,"_104":190,"_23":255,"_106":257,"_140":314},[315],{"_21":299,"_35":36,"_37":38,"_129":130,"_131":252,"_102":300,"_104":300,"_23":301,"_106":302,"_140":316},[],{"_21":236,"_35":259,"_37":260,"_129":130,"_131":245,"_102":246,"_104":246,"_23":261,"_106":264,"_140":318},[319],{"_21":235,"_35":36,"_37":38,"_129":130,"_131":236,"_102":133,"_104":133,"_23":237,"_106":240,"_140":320},[],{"_21":189,"_35":281,"_37":282,"_129":130,"_131":245,"_102":246,"_104":246,"_23":283,"_106":284,"_140":322},[323],{"_21":186,"_35":187,"_37":188,"_129":130,"_131":189,"_102":190,"_104":190,"_23":191,"_106":188,"_140":324},[325],{"_21":275,"_35":36,"_37":38,"_129":130,"_131":186,"_102":276,"_104":276,"_23":277,"_106":279,"_140":326},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários