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

",[199],{"_21":200,"_35":201,"_37":202,"_125":126,"_127":203,"_98":204,"_100":204,"_23":205,"_102":202},"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":206,"_132":133,"_134":207},4,12302,{"_18":209,"_20":19,"_21":210,"_56":211,"_76":223,"_77":224,"_29":225},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[212,215,218,220],{"_21":213,"_60":61,"_62":214},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_21":216,"_60":66,"_62":217},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_21":209,"_60":70,"_62":219},"

Verdadeiro, falso, verdadeiro

",{"_21":221,"_60":74,"_62":222},"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?

",[199],{"_18":227,"_20":19,"_21":228,"_56":229,"_76":244,"_77":245,"_29":246},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[230,233,236,238,241],{"_21":231,"_60":61,"_62":232},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_21":234,"_60":66,"_62":235},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_21":227,"_60":70,"_62":237},"Indeterminado",{"_21":239,"_60":74,"_62":240},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_21":242,"_60":194,"_62":243},"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????",[199],[199,248,257,263,267,268,269,277,282,290,291,296,302],{"_21":249,"_35":250,"_37":251,"_125":126,"_127":252,"_98":142,"_100":142,"_23":253,"_102":256},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_130":254,"_132":133,"_134":255},5,30614,"engenharia-mecatronica-1",{"_21":258,"_35":36,"_37":38,"_125":126,"_127":259,"_98":260,"_100":260,"_23":261,"_102":262},"8850e507-a691-4d45-a7c7-16221e9c5af2","88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T04:00:13.215003+00:00",{"_130":133,"_132":133,"_134":152},"resistencia-dos-materiais-6",{"_21":259,"_35":140,"_37":141,"_125":126,"_127":249,"_98":204,"_100":204,"_23":264,"_102":266},{"_130":254,"_132":133,"_134":265},25741,"mecanica-3",{"_21":122,"_35":123,"_37":124,"_125":126,"_127":-5,"_98":128,"_100":128,"_23":129,"_102":124},{"_21":149,"_35":36,"_37":38,"_125":126,"_127":139,"_98":150,"_100":150,"_23":151,"_102":153},{"_21":270,"_35":271,"_37":272,"_125":126,"_127":252,"_98":142,"_100":142,"_23":273,"_102":276},"b6e37f32-f8e5-4025-bf0f-69ffc00fb331","Engenharia Civil","engenharia-civil",{"_130":274,"_132":133,"_134":275},21,45865,"engenharia-civil-3",{"_21":203,"_35":278,"_37":279,"_125":126,"_127":252,"_98":142,"_100":142,"_23":280,"_102":281},"Engenharia de Petróleo","engenharia-de-petroleo",{"_130":254,"_132":133,"_134":207},"engenharia-de-petroleo-1",{"_21":283,"_35":284,"_37":285,"_125":126,"_127":270,"_98":286,"_100":286,"_23":287,"_102":289},"c5bf57d4-c3d8-4365-b53e-085fa14a3a95","Estruturas","estruturas","2025-04-29T03:44:32.303369+00:00",{"_130":254,"_132":133,"_134":288},8852,"estruturas-1",{"_21":139,"_35":140,"_37":141,"_125":126,"_127":122,"_98":142,"_100":142,"_23":143,"_102":146},{"_21":292,"_35":36,"_37":38,"_125":126,"_127":200,"_98":293,"_100":293,"_23":294,"_102":295},"d1e4567b-f68a-49e1-b3e5-3888343d7871","2025-04-29T04:00:14.680867+00:00",{"_130":133,"_132":133,"_134":152},"resistencia-dos-materiais-7",{"_21":297,"_35":298,"_37":38,"_125":126,"_127":283,"_98":299,"_100":299,"_23":300,"_102":301},"da8d2ecf-e949-4afc-966f-98b4b367fac1","Resistencia dos Materiais","2025-04-29T04:00:06.9766+00:00",{"_130":133,"_132":133,"_134":152},"resistencia-dos-materiais-5",{"_21":252,"_35":303,"_37":304,"_125":126,"_127":-5,"_98":305,"_100":305,"_23":306,"_102":304},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_130":307,"_132":133,"_134":308},29,351586,"tagsTree",[121,311],{"_21":252,"_35":303,"_37":304,"_125":126,"_127":-5,"_98":305,"_100":305,"_23":306,"_102":304,"_136":312},[313,319,325],{"_21":249,"_35":250,"_37":251,"_125":126,"_127":252,"_98":142,"_100":142,"_23":253,"_102":256,"_136":314},[315],{"_21":259,"_35":140,"_37":141,"_125":126,"_127":249,"_98":204,"_100":204,"_23":264,"_102":266,"_136":316},[317],{"_21":258,"_35":36,"_37":38,"_125":126,"_127":259,"_98":260,"_100":260,"_23":261,"_102":262,"_136":318},[],{"_21":270,"_35":271,"_37":272,"_125":126,"_127":252,"_98":142,"_100":142,"_23":273,"_102":276,"_136":320},[321],{"_21":283,"_35":284,"_37":285,"_125":126,"_127":270,"_98":286,"_100":286,"_23":287,"_102":289,"_136":322},[323],{"_21":297,"_35":298,"_37":38,"_125":126,"_127":283,"_98":299,"_100":299,"_23":300,"_102":301,"_136":324},[],{"_21":203,"_35":278,"_37":279,"_125":126,"_127":252,"_98":142,"_100":142,"_23":280,"_102":281,"_136":326},[327],{"_21":200,"_35":201,"_37":202,"_125":126,"_127":203,"_98":204,"_100":204,"_23":205,"_102":202,"_136":328},[329],{"_21":292,"_35":36,"_37":38,"_125":126,"_127":200,"_98":293,"_100":293,"_23":294,"_102":295,"_136":330},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

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