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

",[186],{"_21":187,"_35":188,"_37":189,"_125":126,"_127":190,"_98":191,"_100":191,"_23":192,"_102":189},"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":193,"_133":134,"_135":194},4,12302,{"_18":196,"_20":19,"_21":197,"_56":198,"_76":210,"_77":211,"_29":212},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","93a32dd4-5fc6-4ccb-a76f-4724bf113742",[199,202,205,207],{"_21":200,"_60":61,"_62":201},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_21":203,"_60":66,"_62":204},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_21":196,"_60":70,"_62":206},"

Verdadeiro, falso, verdadeiro

",{"_21":208,"_60":74,"_62":209},"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?

",[213],{"_21":187,"_35":188,"_37":189,"_125":126,"_127":190,"_98":191,"_100":191,"_23":214,"_102":189},{"_131":193,"_133":134,"_135":194},{"_18":216,"_20":19,"_21":217,"_56":218,"_76":233,"_77":234,"_29":235},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[219,222,225,227,230],{"_21":220,"_60":61,"_62":221},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_21":223,"_60":66,"_62":224},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_21":216,"_60":70,"_62":226},"Indeterminado",{"_21":228,"_60":74,"_62":229},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_21":231,"_60":181,"_62":232},"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????",[236],{"_21":187,"_35":188,"_37":189,"_125":126,"_127":190,"_98":191,"_100":191,"_23":237,"_102":189},{"_131":193,"_133":134,"_135":194},[239,241,248,258,265,272,274,282,288,293,299,306],{"_21":187,"_35":188,"_37":189,"_125":126,"_127":190,"_98":191,"_100":191,"_23":240,"_102":189},{"_131":193,"_133":134,"_135":194},{"_21":242,"_35":36,"_37":38,"_125":126,"_127":243,"_98":129,"_100":129,"_23":244,"_102":247},"6b6faf95-0e3a-4f58-abc8-e1444c48041d","92339f4f-ed20-4f4c-ad85-0c3de7e04ae0",{"_131":245,"_133":134,"_135":246},2,11846,"termodinamica-3",{"_21":249,"_35":250,"_37":251,"_125":126,"_127":252,"_98":253,"_100":253,"_23":254,"_102":257},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_131":255,"_133":134,"_135":256},5,30614,"engenharia-mecatronica-1",{"_21":259,"_35":260,"_37":261,"_125":126,"_127":249,"_98":191,"_100":191,"_23":262,"_102":264},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica",{"_131":255,"_133":134,"_135":263},25741,"mecanica-3",{"_21":243,"_35":266,"_37":267,"_125":126,"_127":252,"_98":253,"_100":253,"_23":268,"_102":271},"Engenharia Mecânica","engenharia-mecanica",{"_131":269,"_133":134,"_135":270},11,36318,"engenharia-mecanica-2",{"_21":122,"_35":123,"_37":124,"_125":126,"_127":128,"_98":129,"_100":129,"_23":273,"_102":124},{"_131":132,"_133":134,"_135":136},{"_21":275,"_35":276,"_37":277,"_125":126,"_127":-5,"_98":278,"_100":278,"_23":279,"_102":277},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_131":280,"_133":134,"_135":281},18,135489,{"_21":283,"_35":36,"_37":38,"_125":126,"_127":187,"_98":284,"_100":284,"_23":285,"_102":287},"b21374de-aae5-4a4a-9bf3-0420e731797e","2025-04-29T04:00:14.680867+00:00",{"_131":134,"_133":134,"_135":286},8597,"termodinamica-5",{"_21":190,"_35":289,"_37":290,"_125":126,"_127":252,"_98":253,"_100":253,"_23":291,"_102":292},"Engenharia de Petróleo","engenharia-de-petroleo",{"_131":255,"_133":134,"_135":194},"engenharia-de-petroleo-1",{"_21":128,"_35":294,"_37":295,"_125":126,"_127":275,"_98":253,"_100":253,"_23":296,"_102":298},"Física","fisica",{"_131":269,"_133":134,"_135":297},13777,"fisica-4",{"_21":252,"_35":300,"_37":301,"_125":126,"_127":-5,"_98":302,"_100":302,"_23":303,"_102":301},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_131":304,"_133":134,"_135":305},29,351586,{"_21":307,"_35":36,"_37":38,"_125":126,"_127":259,"_98":308,"_100":308,"_23":309,"_102":310},"f5967cbe-d751-4b40-81f2-04eb5dead2a9","2025-04-29T04:00:13.215003+00:00",{"_131":134,"_133":134,"_135":286},"termodinamica-4","tagsTree",[313,322],{"_21":275,"_35":276,"_37":277,"_125":126,"_127":-5,"_98":278,"_100":278,"_23":314,"_102":277,"_137":315},{"_131":280,"_133":134,"_135":281},[316],{"_21":128,"_35":294,"_37":295,"_125":126,"_127":275,"_98":253,"_100":253,"_23":317,"_102":298,"_137":318},{"_131":269,"_133":134,"_135":297},[319],{"_21":122,"_35":123,"_37":124,"_125":126,"_127":128,"_98":129,"_100":129,"_23":320,"_102":124,"_137":321},{"_131":132,"_133":134,"_135":136},[],{"_21":252,"_35":300,"_37":301,"_125":126,"_127":-5,"_98":302,"_100":302,"_23":323,"_102":301,"_137":324},{"_131":304,"_133":134,"_135":305},[325,334,340],{"_21":249,"_35":250,"_37":251,"_125":126,"_127":252,"_98":253,"_100":253,"_23":326,"_102":257,"_137":327},{"_131":255,"_133":134,"_135":256},[328],{"_21":259,"_35":260,"_37":261,"_125":126,"_127":249,"_98":191,"_100":191,"_23":329,"_102":264,"_137":330},{"_131":255,"_133":134,"_135":263},[331],{"_21":307,"_35":36,"_37":38,"_125":126,"_127":259,"_98":308,"_100":308,"_23":332,"_102":310,"_137":333},{"_131":134,"_133":134,"_135":286},[],{"_21":243,"_35":266,"_37":267,"_125":126,"_127":252,"_98":253,"_100":253,"_23":335,"_102":271,"_137":336},{"_131":269,"_133":134,"_135":270},[337],{"_21":242,"_35":36,"_37":38,"_125":126,"_127":243,"_98":129,"_100":129,"_23":338,"_102":247,"_137":339},{"_131":245,"_133":134,"_135":246},[],{"_21":190,"_35":289,"_37":290,"_125":126,"_127":252,"_98":253,"_100":253,"_23":341,"_102":292,"_137":342},{"_131":255,"_133":134,"_135":194},[343],{"_21":187,"_35":188,"_37":189,"_125":126,"_127":190,"_98":191,"_100":191,"_23":344,"_102":189,"_137":345},{"_131":193,"_133":134,"_135":194},[346],{"_21":283,"_35":36,"_37":38,"_125":126,"_127":187,"_98":284,"_100":284,"_23":347,"_102":287,"_137":348},{"_131":134,"_133":134,"_135":286},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários