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

",[189],{"_21":190,"_35":191,"_37":192,"_129":130,"_131":193,"_102":194,"_104":194,"_23":195,"_106":192},"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":196,"_137":138,"_139":197},4,12302,{"_18":199,"_20":19,"_21":200,"_56":201,"_80":213,"_81":214,"_29":215},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[202,205,208,210],{"_21":203,"_60":61,"_62":204},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_21":206,"_60":66,"_62":207},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_21":199,"_60":70,"_62":209},"

Verdadeiro, falso, verdadeiro

",{"_21":211,"_60":74,"_62":212},"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?

",[216],{"_21":190,"_35":191,"_37":192,"_129":130,"_131":193,"_102":194,"_104":194,"_23":217,"_106":192},{"_135":196,"_137":138,"_139":197},{"_18":219,"_20":19,"_21":220,"_56":221,"_80":236,"_81":237,"_29":238},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[222,225,228,230,233],{"_21":223,"_60":61,"_62":224},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_21":226,"_60":66,"_62":227},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_21":219,"_60":70,"_62":229},"Indeterminado",{"_21":231,"_60":74,"_62":232},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_21":234,"_60":78,"_62":235},"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????",[239],{"_21":190,"_35":191,"_37":192,"_129":130,"_131":193,"_102":194,"_104":194,"_23":240,"_106":192},{"_135":196,"_137":138,"_139":197},[242,244,251,261,268,275,277,285,291,296,302,309],{"_21":190,"_35":191,"_37":192,"_129":130,"_131":193,"_102":194,"_104":194,"_23":243,"_106":192},{"_135":196,"_137":138,"_139":197},{"_21":245,"_35":36,"_37":38,"_129":130,"_131":246,"_102":133,"_104":133,"_23":247,"_106":250},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_135":248,"_137":138,"_139":249},2,11846,"termodinamica-3",{"_21":252,"_35":253,"_37":254,"_129":130,"_131":255,"_102":256,"_104":256,"_23":257,"_106":260},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_135":258,"_137":138,"_139":259},5,30614,"engenharia-mecatronica-1",{"_21":262,"_35":263,"_37":264,"_129":130,"_131":252,"_102":194,"_104":194,"_23":265,"_106":267},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_135":258,"_137":138,"_139":266},25741,"mecanica-3",{"_21":246,"_35":269,"_37":270,"_129":130,"_131":255,"_102":256,"_104":256,"_23":271,"_106":274},"Engenharia Mecânica","engenharia-mecanica",{"_135":272,"_137":138,"_139":273},11,36318,"engenharia-mecanica-2",{"_21":126,"_35":127,"_37":128,"_129":130,"_131":132,"_102":133,"_104":133,"_23":276,"_106":128},{"_135":136,"_137":138,"_139":140},{"_21":278,"_35":279,"_37":280,"_129":130,"_131":-5,"_102":281,"_104":281,"_23":282,"_106":280},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_135":283,"_137":138,"_139":284},18,135489,{"_21":286,"_35":36,"_37":38,"_129":130,"_131":190,"_102":287,"_104":287,"_23":288,"_106":290},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_135":138,"_137":138,"_139":289},8597,"termodinamica-5",{"_21":193,"_35":292,"_37":293,"_129":130,"_131":255,"_102":256,"_104":256,"_23":294,"_106":295},"Engenharia de Petróleo","engenharia-de-petroleo",{"_135":258,"_137":138,"_139":197},"engenharia-de-petroleo-1",{"_21":132,"_35":297,"_37":298,"_129":130,"_131":278,"_102":256,"_104":256,"_23":299,"_106":301},"Física","fisica",{"_135":272,"_137":138,"_139":300},13777,"fisica-4",{"_21":255,"_35":303,"_37":304,"_129":130,"_131":-5,"_102":305,"_104":305,"_23":306,"_106":304},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_135":307,"_137":138,"_139":308},29,351586,{"_21":310,"_35":36,"_37":38,"_129":130,"_131":262,"_102":311,"_104":311,"_23":312,"_106":313},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_135":138,"_137":138,"_139":289},"termodinamica-4","tagsTree",[316,325],{"_21":278,"_35":279,"_37":280,"_129":130,"_131":-5,"_102":281,"_104":281,"_23":317,"_106":280,"_141":318},{"_135":283,"_137":138,"_139":284},[319],{"_21":132,"_35":297,"_37":298,"_129":130,"_131":278,"_102":256,"_104":256,"_23":320,"_106":301,"_141":321},{"_135":272,"_137":138,"_139":300},[322],{"_21":126,"_35":127,"_37":128,"_129":130,"_131":132,"_102":133,"_104":133,"_23":323,"_106":128,"_141":324},{"_135":136,"_137":138,"_139":140},[],{"_21":255,"_35":303,"_37":304,"_129":130,"_131":-5,"_102":305,"_104":305,"_23":326,"_106":304,"_141":327},{"_135":307,"_137":138,"_139":308},[328,337,343],{"_21":252,"_35":253,"_37":254,"_129":130,"_131":255,"_102":256,"_104":256,"_23":329,"_106":260,"_141":330},{"_135":258,"_137":138,"_139":259},[331],{"_21":262,"_35":263,"_37":264,"_129":130,"_131":252,"_102":194,"_104":194,"_23":332,"_106":267,"_141":333},{"_135":258,"_137":138,"_139":266},[334],{"_21":310,"_35":36,"_37":38,"_129":130,"_131":262,"_102":311,"_104":311,"_23":335,"_106":313,"_141":336},{"_135":138,"_137":138,"_139":289},[],{"_21":246,"_35":269,"_37":270,"_129":130,"_131":255,"_102":256,"_104":256,"_23":338,"_106":274,"_141":339},{"_135":272,"_137":138,"_139":273},[340],{"_21":245,"_35":36,"_37":38,"_129":130,"_131":246,"_102":133,"_104":133,"_23":341,"_106":250,"_141":342},{"_135":248,"_137":138,"_139":249},[],{"_21":193,"_35":292,"_37":293,"_129":130,"_131":255,"_102":256,"_104":256,"_23":344,"_106":295,"_141":345},{"_135":258,"_137":138,"_139":197},[346],{"_21":190,"_35":191,"_37":192,"_129":130,"_131":193,"_102":194,"_104":194,"_23":347,"_106":192,"_141":348},{"_135":196,"_137":138,"_139":197},[349],{"_21":286,"_35":36,"_37":38,"_129":130,"_131":190,"_102":287,"_104":287,"_23":350,"_106":290,"_141":351},{"_135":138,"_137":138,"_139":289},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários