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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],{"_21":183,"_34":184,"_36":185,"_124":125,"_126":186,"_97":187,"_99":187,"_23":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":19,"_21":193,"_55":194,"_75":206,"_76":207,"_28":208},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[195,198,201,203],{"_21":196,"_59":60,"_61":197},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_21":199,"_59":65,"_61":200},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_21":192,"_59":69,"_61":202},"

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?

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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],[182,231,237,247,254,261,262,270,276,281,287,294],{"_21":232,"_34":35,"_36":37,"_124":125,"_126":233,"_97":128,"_99":128,"_23":234,"_101":236},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_130":41,"_132":133,"_134":235},11846,"termodinamica-3",{"_21":238,"_34":239,"_36":240,"_124":125,"_126":241,"_97":242,"_99":242,"_23":243,"_101":246},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_130":244,"_132":133,"_134":245},5,30614,"engenharia-mecatronica-1",{"_21":248,"_34":249,"_36":250,"_124":125,"_126":238,"_97":187,"_99":187,"_23":251,"_101":253},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_130":244,"_132":133,"_134":252},25741,"mecanica-3",{"_21":233,"_34":255,"_36":256,"_124":125,"_126":241,"_97":242,"_99":242,"_23":257,"_101":260},"Engenharia Mecânica","engenharia-mecanica",{"_130":258,"_132":133,"_134":259},11,36318,"engenharia-mecanica-2",{"_21":121,"_34":122,"_36":123,"_124":125,"_126":127,"_97":128,"_99":128,"_23":129,"_101":123},{"_21":263,"_34":264,"_36":265,"_124":125,"_126":-5,"_97":266,"_99":266,"_23":267,"_101":265},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_130":268,"_132":133,"_134":269},18,135489,{"_21":271,"_34":35,"_36":37,"_124":125,"_126":183,"_97":272,"_99":272,"_23":273,"_101":275},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_130":133,"_132":133,"_134":274},8597,"termodinamica-5",{"_21":186,"_34":277,"_36":278,"_124":125,"_126":241,"_97":242,"_99":242,"_23":279,"_101":280},"Engenharia de Petróleo","engenharia-de-petroleo",{"_130":244,"_132":133,"_134":190},"engenharia-de-petroleo-1",{"_21":127,"_34":282,"_36":283,"_124":125,"_126":263,"_97":242,"_99":242,"_23":284,"_101":286},"Física","fisica",{"_130":258,"_132":133,"_134":285},13777,"fisica-4",{"_21":241,"_34":288,"_36":289,"_124":125,"_126":-5,"_97":290,"_99":290,"_23":291,"_101":289},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_130":292,"_132":133,"_134":293},29,351586,{"_21":295,"_34":35,"_36":37,"_124":125,"_126":248,"_97":296,"_99":296,"_23":297,"_101":298},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_130":133,"_132":133,"_134":274},"termodinamica-4","tagsTree",[301,305],{"_21":263,"_34":264,"_36":265,"_124":125,"_126":-5,"_97":266,"_99":266,"_23":267,"_101":265,"_136":302},[303],{"_21":127,"_34":282,"_36":283,"_124":125,"_126":263,"_97":242,"_99":242,"_23":284,"_101":286,"_136":304},[120],{"_21":241,"_34":288,"_36":289,"_124":125,"_126":-5,"_97":290,"_99":290,"_23":291,"_101":289,"_136":306},[307,313,317],{"_21":238,"_34":239,"_36":240,"_124":125,"_126":241,"_97":242,"_99":242,"_23":243,"_101":246,"_136":308},[309],{"_21":248,"_34":249,"_36":250,"_124":125,"_126":238,"_97":187,"_99":187,"_23":251,"_101":253,"_136":310},[311],{"_21":295,"_34":35,"_36":37,"_124":125,"_126":248,"_97":296,"_99":296,"_23":297,"_101":298,"_136":312},[],{"_21":233,"_34":255,"_36":256,"_124":125,"_126":241,"_97":242,"_99":242,"_23":257,"_101":260,"_136":314},[315],{"_21":232,"_34":35,"_36":37,"_124":125,"_126":233,"_97":128,"_99":128,"_23":234,"_101":236,"_136":316},[],{"_21":186,"_34":277,"_36":278,"_124":125,"_126":241,"_97":242,"_99":242,"_23":279,"_101":280,"_136":318},[319],{"_21":183,"_34":184,"_36":185,"_124":125,"_126":186,"_97":187,"_99":187,"_23":188,"_101":185,"_136":320},[321],{"_21":271,"_34":35,"_36":37,"_124":125,"_126":183,"_97":272,"_99":272,"_23":273,"_101":275,"_136":322},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários