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

",[185],{"_21":186,"_35":187,"_37":188,"_125":126,"_127":189,"_98":190,"_100":190,"_23":191,"_102":188},"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":192,"_133":42,"_134":193},4,12302,{"_18":195,"_20":19,"_21":196,"_56":197,"_76":209,"_77":210,"_29":211},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[198,201,204,206],{"_21":199,"_60":61,"_62":200},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_21":202,"_60":66,"_62":203},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_21":195,"_60":70,"_62":205},"

Verdadeiro, falso, verdadeiro

",{"_21":207,"_60":74,"_62":208},"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?

",[212],{"_21":186,"_35":187,"_37":188,"_125":126,"_127":189,"_98":190,"_100":190,"_23":213,"_102":188},{"_131":192,"_133":42,"_134":193},{"_18":215,"_20":19,"_21":216,"_56":217,"_76":232,"_77":233,"_29":234},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[218,221,224,226,229],{"_21":219,"_60":61,"_62":220},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_21":222,"_60":66,"_62":223},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_21":215,"_60":70,"_62":225},"Indeterminado",{"_21":227,"_60":74,"_62":228},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_21":230,"_60":180,"_62":231},"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????",[235],{"_21":186,"_35":187,"_37":188,"_125":126,"_127":189,"_98":190,"_100":190,"_23":236,"_102":188},{"_131":192,"_133":42,"_134":193},[238,240,247,257,264,271,273,281,287,292,298,305],{"_21":186,"_35":187,"_37":188,"_125":126,"_127":189,"_98":190,"_100":190,"_23":239,"_102":188},{"_131":192,"_133":42,"_134":193},{"_21":241,"_35":36,"_37":38,"_125":126,"_127":242,"_98":129,"_100":129,"_23":243,"_102":246},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_131":244,"_133":42,"_134":245},2,11846,"termodinamica-3",{"_21":248,"_35":249,"_37":250,"_125":126,"_127":251,"_98":252,"_100":252,"_23":253,"_102":256},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_131":254,"_133":42,"_134":255},5,30614,"engenharia-mecatronica-1",{"_21":258,"_35":259,"_37":260,"_125":126,"_127":248,"_98":190,"_100":190,"_23":261,"_102":263},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_131":254,"_133":42,"_134":262},25741,"mecanica-3",{"_21":242,"_35":265,"_37":266,"_125":126,"_127":251,"_98":252,"_100":252,"_23":267,"_102":270},"Engenharia Mecânica","engenharia-mecanica",{"_131":268,"_133":42,"_134":269},11,36318,"engenharia-mecanica-2",{"_21":122,"_35":123,"_37":124,"_125":126,"_127":128,"_98":129,"_100":129,"_23":272,"_102":124},{"_131":132,"_133":42,"_134":135},{"_21":274,"_35":275,"_37":276,"_125":126,"_127":-5,"_98":277,"_100":277,"_23":278,"_102":276},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_131":279,"_133":42,"_134":280},18,135489,{"_21":282,"_35":36,"_37":38,"_125":126,"_127":186,"_98":283,"_100":283,"_23":284,"_102":286},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_131":42,"_133":42,"_134":285},8597,"termodinamica-5",{"_21":189,"_35":288,"_37":289,"_125":126,"_127":251,"_98":252,"_100":252,"_23":290,"_102":291},"Engenharia de Petróleo","engenharia-de-petroleo",{"_131":254,"_133":42,"_134":193},"engenharia-de-petroleo-1",{"_21":128,"_35":293,"_37":294,"_125":126,"_127":274,"_98":252,"_100":252,"_23":295,"_102":297},"Física","fisica",{"_131":268,"_133":42,"_134":296},13777,"fisica-4",{"_21":251,"_35":299,"_37":300,"_125":126,"_127":-5,"_98":301,"_100":301,"_23":302,"_102":300},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_131":303,"_133":42,"_134":304},29,351586,{"_21":306,"_35":36,"_37":38,"_125":126,"_127":258,"_98":307,"_100":307,"_23":308,"_102":309},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_131":42,"_133":42,"_134":285},"termodinamica-4","tagsTree",[312,321],{"_21":274,"_35":275,"_37":276,"_125":126,"_127":-5,"_98":277,"_100":277,"_23":313,"_102":276,"_136":314},{"_131":279,"_133":42,"_134":280},[315],{"_21":128,"_35":293,"_37":294,"_125":126,"_127":274,"_98":252,"_100":252,"_23":316,"_102":297,"_136":317},{"_131":268,"_133":42,"_134":296},[318],{"_21":122,"_35":123,"_37":124,"_125":126,"_127":128,"_98":129,"_100":129,"_23":319,"_102":124,"_136":320},{"_131":132,"_133":42,"_134":135},[],{"_21":251,"_35":299,"_37":300,"_125":126,"_127":-5,"_98":301,"_100":301,"_23":322,"_102":300,"_136":323},{"_131":303,"_133":42,"_134":304},[324,333,339],{"_21":248,"_35":249,"_37":250,"_125":126,"_127":251,"_98":252,"_100":252,"_23":325,"_102":256,"_136":326},{"_131":254,"_133":42,"_134":255},[327],{"_21":258,"_35":259,"_37":260,"_125":126,"_127":248,"_98":190,"_100":190,"_23":328,"_102":263,"_136":329},{"_131":254,"_133":42,"_134":262},[330],{"_21":306,"_35":36,"_37":38,"_125":126,"_127":258,"_98":307,"_100":307,"_23":331,"_102":309,"_136":332},{"_131":42,"_133":42,"_134":285},[],{"_21":242,"_35":265,"_37":266,"_125":126,"_127":251,"_98":252,"_100":252,"_23":334,"_102":270,"_136":335},{"_131":268,"_133":42,"_134":269},[336],{"_21":241,"_35":36,"_37":38,"_125":126,"_127":242,"_98":129,"_100":129,"_23":337,"_102":246,"_136":338},{"_131":244,"_133":42,"_134":245},[],{"_21":189,"_35":288,"_37":289,"_125":126,"_127":251,"_98":252,"_100":252,"_23":340,"_102":291,"_136":341},{"_131":254,"_133":42,"_134":193},[342],{"_21":186,"_35":187,"_37":188,"_125":126,"_127":189,"_98":190,"_100":190,"_23":343,"_102":188,"_136":344},{"_131":192,"_133":42,"_134":193},[345],{"_21":282,"_35":36,"_37":38,"_125":126,"_127":186,"_98":283,"_100":283,"_23":346,"_102":286,"_136":347},{"_131":42,"_133":42,"_134":285},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários