Use eigenvalue metnoa to nna requireasolution of the following system.x₁x2 = −4x₁3x2 – £3 and-x3= 2x1 + x2 = x3O== 4x₁ + 4x2 + 2x3. The initialconditions are ₁ (0) = 0, x2 (0) = 1and 3 (0) = 4.2-8-8-0-2 + sin 2t -2 +e² 37x(t) = cos 2t6642H H+O-5 +e²t 43x(t) = cos 3t -3 + sin 3tx(t) = cos 3tx(t) = cos 2t2-#-#-D-2 + sin 3t342-6-4 + sin 2t632tel+ e0

Answered: Image /qna-images/answer/c53b0e10-56b3-4136-ade7-ce99bcc5244b.jpg

Answered: Use eigenvalue metnoa to nina requirea…

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 d²x dt² d²y dt2 =x+3y, The coefficient matrix 1 3 3 3x+y. wwwwww has eigenvectors Hand [1] are 4 and - 2. Select the option that gives the general solution of this system. Select one: ° 1) = 0[¹] con (24) + C₁ [₁] (²0₁₁+₂ [1¹] CA cos(2t) sin(2t) + C3 ev2t [*] = C₁ [1] cos(2t) + 0₂ sin(2t) + C3 cos(√2t) + C4 Casin(√21) = + HHH] co √21) + C [¹] sin (√2) C₁ e2t cos(√2t) C4 C3 and the corresponding eigenvalues [3] = C₁ [1] cos(2t) + C₂ e2t 2t [1] = ₂ [1] ² + ₂ [1] ² ² + ₁ [₁¹] e√²+ + C₁ [ 1¹ ] e-√₂² 2t e C4 A WEW MEXAND sin(2t) + C3 · [₁¹] ₁ √²+ + 0₁ [1¹] ₁ = √² √√2t e
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