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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

",[132,150,158,166,172],{"_19":133,"_56":134,"_135":136,"_137":138,"_139":140,"_68":141,"_70":141,"_64":142,"_148":149},"861ad829-750d-4a44-9569-2f18b430b4df","Engenharia Mecatrônica","alias","engenharia-mecatronica","tag_group_id","c1ce2cf2-b217-4cc7-8182-81c56bd3522d","parent_id","eb9315c5-bd04-4116-aa46-02c4fde320c0","2025-04-29T02:19:12.828432+00:00",{"_143":144,"_145":106,"_146":147},"childrenCount",5,"content_count","question_count",30614,"slug","engenharia-mecatronica-1",{"_19":151,"_56":152,"_135":153,"_137":138,"_139":133,"_68":154,"_70":154,"_64":155,"_148":157},"88fe96b3-2a17-4198-90d5-ddda3d6f5d45","Mecânica","mecanica","2025-04-29T03:44:35.328997+00:00",{"_143":144,"_145":106,"_146":156},25741,"mecanica-3",{"_19":159,"_56":160,"_135":161,"_137":138,"_139":-5,"_68":162,"_70":162,"_64":163,"_148":161},"9772e958-72c6-4499-ad47-877cf94d670d","Exatas","exatas","2025-04-29T01:56:45.284172+00:00",{"_143":164,"_145":106,"_146":165},18,135489,{"_19":167,"_56":152,"_135":153,"_137":138,"_139":159,"_68":141,"_70":141,"_64":168,"_148":171},"ca6fee0e-79c6-4f1c-b500-ee081a071949",{"_143":169,"_145":106,"_146":170},10,19948,"mecanica-2",{"_19":140,"_56":173,"_135":174,"_137":138,"_139":-5,"_68":175,"_70":175,"_64":176,"_148":174},"Engenharia","engenharia","2025-04-29T01:55:38.635246+00:00",{"_143":177,"_145":106,"_146":178},29,351586,{"_16":17,"_18":17,"_19":180,"_21":181,"_45":17,"_46":194,"_88":195},"4a3f20e5-655d-4a84-bbdf-aa3b0de4581a",[182,185,188,191],{"_19":183,"_25":26,"_27":184},"8dee6a5e-57a3-4743-8b5a-da9b8c54fb32","Verdadero, verdadero, verdadero, verdadero.",{"_19":186,"_25":31,"_27":187},"ca0a9b0d-3004-478e-9ca9-bafa5243aca9","Verdadero, verdadero, falso, verdadero.",{"_19":189,"_25":35,"_27":190},"68712800-8b4b-46af-9cdf-3f83e4032c30","Verdadero, falso, verdadero, falso.",{"_19":192,"_25":39,"_27":193},"1f5e395b-c362-4503-8261-dcfcae96b1ce","Falso, verdadero, verdadeiro, verdadeiro.","

Divide el polinomio p(x) = 3x^4 + 4x^3 + x^2 entre el polinomio q(x) = 2+x. Como el polinomio divisor, q(x), es de grado 2, debemos encontrar dos polinomios, un polinomio cociente (c(x)) y un polinomio resto (r(x)) de grado 1 o 0, tales que p(x) = q(x) * c(x) + r(x).

El polinomio p(x) es de grado 4.

El polinomio q(x) es de grado 1.

El polinomio cociente c(x) es de grado 2.

El polinomio resto r(x) es de grado 1 o 0.

",[132,150,158,166,172],{"_16":17,"_18":17,"_19":197,"_21":198,"_45":17,"_46":211,"_88":212},"93a32dd4-5fc6-4ccb-a76f-4724bf113742",[199,202,205,208],{"_19":200,"_25":26,"_27":201},"13e3f476-a0a5-421f-b47e-0969e8e9a7e0","

Verdadeiro, verdadeiro, falso

",{"_19":203,"_25":31,"_27":204},"c9a20855-d84b-4860-8b35-9784818282cf","

Falso, verdadeiro, verdadeiro

",{"_19":206,"_25":35,"_27":207},"6831a9b9-c9a4-4a76-bd7a-2ce98bfea875","

Verdadeiro, falso, verdadeiro

",{"_19":209,"_25":39,"_27":210},"3c98539b-1af9-4d44-aecd-c266754a2075","

Falso, falso, falso

","

Qual é a idade da madeira na qual 85,5\\% do C-14 se decompos?

",[132,150,158,166,172],{"_16":17,"_18":17,"_19":214,"_21":215,"_45":17,"_46":231,"_88":232},"996628fc-4ac3-4821-86bd-839f86a97a6d",[216,219,222,225,228],{"_19":217,"_25":26,"_27":218},"5ad09994-6dcb-4c66-87ae-ec00e9b439b7","5 + 3x < 2x + 4",{"_19":220,"_25":31,"_27":221},"b3ae9948-890b-4807-b801-1e1888cb0c10","3 + 4x \\leq 8x + 6",{"_19":223,"_25":35,"_27":224},"d2964603-f26c-4be6-99ae-d174678f104c","5 + 4x > 3x + 2",{"_19":226,"_25":39,"_27":227},"88c48b1a-ce37-4eae-a900-a4fb4bd581d9","1 + 3x \\geq 5x + 7",{"_19":229,"_25":43,"_27":230},"155e0bb0-6c7f-4d9c-96e5-d1cdb97c632b","4(3 + 2x) < -(6x + 8)","Resolver las siguientes inecuaciones y representar la solución en la recta real:",[132,150,158,166,172],{"_16":17,"_18":17,"_19":234,"_21":235,"_45":17,"_46":251,"_88":252},"c478a46c-46a8-4942-ae14-2e79def3dda2",[236,239,242,245,248],{"_19":237,"_25":26,"_27":238},"a5a16a42-3e58-4c76-80f2-c291aa2d8e49","Sim",{"_19":240,"_25":31,"_27":241},"5e6d0254-696c-4da0-b572-82e3a19f433e","Não",{"_19":243,"_25":35,"_27":244},"3ce109b1-6cdb-4b4d-8816-a6af4d74bed0","Indeterminado",{"_19":246,"_25":39,"_27":247},"35403f68-a880-429d-97f4-db507c58de38","Todos",{"_19":249,"_25":43,"_27":250},"2e06d948-d37e-4350-afc7-ced04941bcaf","Nenhum","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????",[132,150,158,166,172],[132,150,158,166,172],"tagsTree",[256,261],{"_19":159,"_56":160,"_135":161,"_137":138,"_139":-5,"_68":162,"_70":162,"_64":163,"_148":161,"_257":258},"children",[259],{"_19":167,"_56":152,"_135":153,"_137":138,"_139":159,"_68":141,"_70":141,"_64":168,"_148":171,"_257":260},[],{"_19":140,"_56":173,"_135":174,"_137":138,"_139":-5,"_68":175,"_70":175,"_64":176,"_148":174,"_257":262},[263],{"_19":133,"_56":134,"_135":136,"_137":138,"_139":140,"_68":141,"_70":141,"_64":142,"_148":149,"_257":264},[265],{"_19":151,"_56":152,"_135":153,"_137":138,"_139":133,"_68":154,"_70":154,"_64":155,"_148":157,"_257":266},[],"videoDislikes",{},"videoLikes",{},"actionData","errors"]

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