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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,"_125":126,"_127":193,"_98":139,"_100":139,"_23":194,"_102":197},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","engenharia-mecatronica","eb9315c5-bd04-4116-aa46-02c4fde320c0",{"_130":195,"_132":42,"_133":196},5,30614,"engenharia-mecatronica-1",{"_18":199,"_20":19,"_21":200,"_56":201,"_76":213,"_77":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?

",[189],{"_18":217,"_20":19,"_21":218,"_56":219,"_76":234,"_77":235,"_29":236},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","c478a46c-46a8-4942-ae14-2e79def3dda2",[220,223,226,228,231],{"_21":221,"_60":61,"_62":222},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_21":224,"_60":66,"_62":225},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_21":217,"_60":70,"_62":227},"Indeterminado",{"_21":229,"_60":74,"_62":230},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_21":232,"_60":184,"_62":233},"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????",[189],[189,238,244,245,246],{"_21":239,"_35":36,"_37":38,"_125":126,"_127":190,"_98":240,"_100":240,"_23":241,"_102":243},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","2025-04-29T03:44:35.328997+00:00",{"_130":195,"_132":42,"_133":242},25741,"mecanica-3",{"_21":122,"_35":123,"_37":124,"_125":126,"_127":-5,"_98":128,"_100":128,"_23":129,"_102":124},{"_21":138,"_35":36,"_37":38,"_125":126,"_127":122,"_98":139,"_100":139,"_23":140,"_102":143},{"_21":193,"_35":247,"_37":248,"_125":126,"_127":-5,"_98":249,"_100":249,"_23":250,"_102":248},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_130":251,"_132":42,"_133":252},29,351586,"tagsTree",[121,255],{"_21":193,"_35":247,"_37":248,"_125":126,"_127":-5,"_98":249,"_100":249,"_23":250,"_102":248,"_135":256},[257],{"_21":190,"_35":191,"_37":192,"_125":126,"_127":193,"_98":139,"_100":139,"_23":194,"_102":197,"_135":258},[259],{"_21":239,"_35":36,"_37":38,"_125":126,"_127":190,"_98":240,"_100":240,"_23":241,"_102":243,"_135":260},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

Comentários