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Consider the second-order system of differential equations d'y dt² d²x dt² The coefficient matrix = x - 5y, O Select one: O eigenvalues are 6 and -4. Select the option that gives the general solution of this system. [3] [3] 1 C₁ = C₁ H = -5x+y. [:]-[₁] (√) + C₂ [₁] «in(v) + Cs [] cos(21) + Cain (2) cos(√6t) sin(√6t) C3 H D](21) + C₂ 1 evot has eigenvectors C₁ [:]-[₁] = cos(√6t) + C₂ e H cos(√6t) + C₂ and 6t + C3 sin (√6t) + C3 [1₁] sin and the corresponding HHHH ev²e + C₂ [1¹₁] c + a₂ [1] ² + a₂ [¹] evot -√6t e C3 CA cos(2t) + C4 H₁ 1 [¹₁] [¹₁] e2t + C4 sin (√6t) + C3 e ₂ sin(2t) -2t o-2t e - 0₂ [H] ₁² + a₂ He e²t C4

Consider the second-order system of differential equations d'y dt² d²x dt² The coefficient matrix = x - 5y, O Select one: O eigenvalues are 6 and -4. Select the option that gives the general solution of this system. [3] [3] 1 C₁ = C₁ H = -5x+y. [:]-[₁] (√) + C₂ [₁] «in(v) + Cs [] cos(21) + Cain (2) cos(√6t) sin(√6t) C3 H D](21) + C₂ 1 evot has eigenvectors C₁ [:]-[₁] = cos(√6t) + C₂ e H cos(√6t) + C₂ and 6t + C3 sin (√6t) + C3 [1₁] sin and the corresponding HHHH ev²e + C₂ [1¹₁] c + a₂ [1] ² + a₂ [¹] evot -√6t e C3 CA cos(2t) + C4 H₁ 1 [¹₁] [¹₁] e2t + C4 sin (√6t) + C3 e ₂ sin(2t) -2t o-2t e - 0₂ [H] ₁² + a₂ He e²t C4

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the second-order system of differential equations dy d²x dt² =x-5y, The coefficient matrix 1 -5 eigenvalues are 6 and -4. Select the option that gives the general solution of this system. I dt² C₁ -5x + y. 1 -5 11 1 has eigenvectors Select one: [*] = C₁ [ ¹₁ ] cos(√õt) + C₂ [ ¹₁ ] sin(√6t) + Cs [1] cos(2t) + C₁ [1] C3 C4 sin(2t) evot + Vot C3 - [3] = a₁ [¹₁] ev [*] = C₁ [1] cos(√ēt) + C₂ H ₂[1] HHHHH [+] = C₁₂ [ ¹₁ ] ev√² + C₂ [ ¹₁ ] e-√₂ 3 [1] 2²¹ -C₂₁ [ ²₁ ] e-√² + C₂ [1] sin(√6t) + C3 [1₁] [1] Cos evot +03 e2t+CA C₂ [4] [1] and H cos(√6t) + C₂ and the corresponding cos(2t) + C4 H e2t + C4 sin(2t) -2t [¹1] e ²2 -2t e2t sin (√6t) + C3 as He" + a₁₂H₁² -2t
Transcribed Image Text:Consider the second-order system of differential equations dy d²x dt² =x-5y, The coefficient matrix 1 -5 eigenvalues are 6 and -4. Select the option that gives the general solution of this system. I dt² C₁ -5x + y. 1 -5 11 1 has eigenvectors Select one: [*] = C₁ [ ¹₁ ] cos(√õt) + C₂ [ ¹₁ ] sin(√6t) + Cs [1] cos(2t) + C₁ [1] C3 C4 sin(2t) evot + Vot C3 - [3] = a₁ [¹₁] ev [*] = C₁ [1] cos(√ēt) + C₂ H ₂[1] HHHHH [+] = C₁₂ [ ¹₁ ] ev√² + C₂ [ ¹₁ ] e-√₂ 3 [1] 2²¹ -C₂₁ [ ²₁ ] e-√² + C₂ [1] sin(√6t) + C3 [1₁] [1] Cos evot +03 e2t+CA C₂ [4] [1] and H cos(√6t) + C₂ and the corresponding cos(2t) + C4 H e2t + C4 sin(2t) -2t [¹1] e ²2 -2t e2t sin (√6t) + C3 as He" + a₁₂H₁² -2t
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