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,"_35":184,"_37":185,"_125":126,"_127":186,"_98":187,"_100":187,"_23":188,"_102":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",{"_131":189,"_133":42,"_134":190},4,12302,{"_18":192,"_20":19,"_21":193,"_56":194,"_76":206,"_77":207,"_29":208},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[195,198,201,203],{"_21":196,"_60":61,"_62":197},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_21":199,"_60":66,"_62":200},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_21":192,"_60":70,"_62":202},"

Verdadeiro, falso, verdadeiro

",{"_21":204,"_60":74,"_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?

",[182],{"_18":210,"_20":19,"_21":211,"_56":212,"_76":227,"_77":228,"_29":229},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[213,216,219,221,224],{"_21":214,"_60":61,"_62":215},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_21":217,"_60":66,"_62":218},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_21":210,"_60":70,"_62":220},"Indeterminado",{"_21":222,"_60":74,"_62":223},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_21":225,"_60":177,"_62":226},"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????",[182],[182,231,238,248,255,262,263,271,277,282,288,295],{"_21":232,"_35":36,"_37":38,"_125":126,"_127":233,"_98":129,"_100":129,"_23":234,"_102":237},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_131":235,"_133":42,"_134":236},2,11846,"termodinamica-3",{"_21":239,"_35":240,"_37":241,"_125":126,"_127":242,"_98":243,"_100":243,"_23":244,"_102":247},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_131":245,"_133":42,"_134":246},5,30614,"engenharia-mecatronica-1",{"_21":249,"_35":250,"_37":251,"_125":126,"_127":239,"_98":187,"_100":187,"_23":252,"_102":254},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_131":245,"_133":42,"_134":253},25741,"mecanica-3",{"_21":233,"_35":256,"_37":257,"_125":126,"_127":242,"_98":243,"_100":243,"_23":258,"_102":261},"Engenharia Mecânica","engenharia-mecanica",{"_131":259,"_133":42,"_134":260},11,36318,"engenharia-mecanica-2",{"_21":122,"_35":123,"_37":124,"_125":126,"_127":128,"_98":129,"_100":129,"_23":130,"_102":124},{"_21":264,"_35":265,"_37":266,"_125":126,"_127":-5,"_98":267,"_100":267,"_23":268,"_102":266},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_131":269,"_133":42,"_134":270},18,135489,{"_21":272,"_35":36,"_37":38,"_125":126,"_127":183,"_98":273,"_100":273,"_23":274,"_102":276},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_131":42,"_133":42,"_134":275},8597,"termodinamica-5",{"_21":186,"_35":278,"_37":279,"_125":126,"_127":242,"_98":243,"_100":243,"_23":280,"_102":281},"Engenharia de Petróleo","engenharia-de-petroleo",{"_131":245,"_133":42,"_134":190},"engenharia-de-petroleo-1",{"_21":128,"_35":283,"_37":284,"_125":126,"_127":264,"_98":243,"_100":243,"_23":285,"_102":287},"Física","fisica",{"_131":259,"_133":42,"_134":286},13777,"fisica-4",{"_21":242,"_35":289,"_37":290,"_125":126,"_127":-5,"_98":291,"_100":291,"_23":292,"_102":290},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_131":293,"_133":42,"_134":294},29,351586,{"_21":296,"_35":36,"_37":38,"_125":126,"_127":249,"_98":297,"_100":297,"_23":298,"_102":299},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_131":42,"_133":42,"_134":275},"termodinamica-4","tagsTree",[302,306],{"_21":264,"_35":265,"_37":266,"_125":126,"_127":-5,"_98":267,"_100":267,"_23":268,"_102":266,"_136":303},[304],{"_21":128,"_35":283,"_37":284,"_125":126,"_127":264,"_98":243,"_100":243,"_23":285,"_102":287,"_136":305},[121],{"_21":242,"_35":289,"_37":290,"_125":126,"_127":-5,"_98":291,"_100":291,"_23":292,"_102":290,"_136":307},[308,314,318],{"_21":239,"_35":240,"_37":241,"_125":126,"_127":242,"_98":243,"_100":243,"_23":244,"_102":247,"_136":309},[310],{"_21":249,"_35":250,"_37":251,"_125":126,"_127":239,"_98":187,"_100":187,"_23":252,"_102":254,"_136":311},[312],{"_21":296,"_35":36,"_37":38,"_125":126,"_127":249,"_98":297,"_100":297,"_23":298,"_102":299,"_136":313},[],{"_21":233,"_35":256,"_37":257,"_125":126,"_127":242,"_98":243,"_100":243,"_23":258,"_102":261,"_136":315},[316],{"_21":232,"_35":36,"_37":38,"_125":126,"_127":233,"_98":129,"_100":129,"_23":234,"_102":237,"_136":317},[],{"_21":186,"_35":278,"_37":279,"_125":126,"_127":242,"_98":243,"_100":243,"_23":280,"_102":281,"_136":319},[320],{"_21":183,"_35":184,"_37":185,"_125":126,"_127":186,"_98":187,"_100":187,"_23":188,"_102":185,"_136":321},[322],{"_21":272,"_35":36,"_37":38,"_125":126,"_127":183,"_98":273,"_100":273,"_23":274,"_102":276,"_136":323},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários