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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

",[182],{"_22":183,"_35":184,"_37":185,"_124":125,"_126":186,"_97":187,"_99":187,"_24":188,"_101":185},"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",{"_130":189,"_132":133,"_134":190},4,12302,{"_18":192,"_20":21,"_22":193,"_56":194,"_75":206,"_76":207,"_29":208},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[195,198,201,203],{"_22":196,"_60":61,"_62":197},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_22":199,"_60":66,"_62":200},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_22":192,"_60":70,"_62":202},"

Verdadeiro, falso, verdadeiro

",{"_22":204,"_60":73,"_62":205},"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????",[182],[182,231,238,248,255,262,263,271,277,282,288,295],{"_22":232,"_35":36,"_37":38,"_124":125,"_126":233,"_97":128,"_99":128,"_24":234,"_101":237},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_130":235,"_132":133,"_134":236},2,11846,"termodinamica-3",{"_22":239,"_35":240,"_37":241,"_124":125,"_126":242,"_97":243,"_99":243,"_24":244,"_101":247},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_130":245,"_132":133,"_134":246},5,30614,"engenharia-mecatronica-1",{"_22":249,"_35":250,"_37":251,"_124":125,"_126":239,"_97":187,"_99":187,"_24":252,"_101":254},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_130":245,"_132":133,"_134":253},25741,"mecanica-3",{"_22":233,"_35":256,"_37":257,"_124":125,"_126":242,"_97":243,"_99":243,"_24":258,"_101":261},"Engenharia Mecânica","engenharia-mecanica",{"_130":259,"_132":133,"_134":260},11,36318,"engenharia-mecanica-2",{"_22":121,"_35":122,"_37":123,"_124":125,"_126":127,"_97":128,"_99":128,"_24":129,"_101":123},{"_22":264,"_35":265,"_37":266,"_124":125,"_126":-5,"_97":267,"_99":267,"_24":268,"_101":266},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_130":269,"_132":133,"_134":270},18,135489,{"_22":272,"_35":36,"_37":38,"_124":125,"_126":183,"_97":273,"_99":273,"_24":274,"_101":276},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_130":133,"_132":133,"_134":275},8597,"termodinamica-5",{"_22":186,"_35":278,"_37":279,"_124":125,"_126":242,"_97":243,"_99":243,"_24":280,"_101":281},"Engenharia de Petróleo","engenharia-de-petroleo",{"_130":245,"_132":133,"_134":190},"engenharia-de-petroleo-1",{"_22":127,"_35":283,"_37":284,"_124":125,"_126":264,"_97":243,"_99":243,"_24":285,"_101":287},"Física","fisica",{"_130":259,"_132":133,"_134":286},13777,"fisica-4",{"_22":242,"_35":289,"_37":290,"_124":125,"_126":-5,"_97":291,"_99":291,"_24":292,"_101":290},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_130":293,"_132":133,"_134":294},29,351586,{"_22":296,"_35":36,"_37":38,"_124":125,"_126":249,"_97":297,"_99":297,"_24":298,"_101":299},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_130":133,"_132":133,"_134":275},"termodinamica-4","tagsTree",[302,306],{"_22":264,"_35":265,"_37":266,"_124":125,"_126":-5,"_97":267,"_99":267,"_24":268,"_101":266,"_136":303},[304],{"_22":127,"_35":283,"_37":284,"_124":125,"_126":264,"_97":243,"_99":243,"_24":285,"_101":287,"_136":305},[120],{"_22":242,"_35":289,"_37":290,"_124":125,"_126":-5,"_97":291,"_99":291,"_24":292,"_101":290,"_136":307},[308,314,318],{"_22":239,"_35":240,"_37":241,"_124":125,"_126":242,"_97":243,"_99":243,"_24":244,"_101":247,"_136":309},[310],{"_22":249,"_35":250,"_37":251,"_124":125,"_126":239,"_97":187,"_99":187,"_24":252,"_101":254,"_136":311},[312],{"_22":296,"_35":36,"_37":38,"_124":125,"_126":249,"_97":297,"_99":297,"_24":298,"_101":299,"_136":313},[],{"_22":233,"_35":256,"_37":257,"_124":125,"_126":242,"_97":243,"_99":243,"_24":258,"_101":261,"_136":315},[316],{"_22":232,"_35":36,"_37":38,"_124":125,"_126":233,"_97":128,"_99":128,"_24":234,"_101":237,"_136":317},[],{"_22":186,"_35":278,"_37":279,"_124":125,"_126":242,"_97":243,"_99":243,"_24":280,"_101":281,"_136":319},[320],{"_22":183,"_35":184,"_37":185,"_124":125,"_126":186,"_97":187,"_99":187,"_24":188,"_101":185,"_136":321},[322],{"_22":272,"_35":36,"_37":38,"_124":125,"_126":183,"_97":273,"_99":273,"_24":274,"_101":276,"_136":323},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários