Given the initial value problem x – 6x1 + x2 = 0 x, – 5x1 – 4x2 = 0 T, (0) — - 2, г2(0) — 0 %3D find 12(t). O r2(t) = 2e5t (cos (2t) + sin (2t)) O r2(t) = e5t (cos (2t) + sin (2t)) O r2(t) = e5t sin (2t) O 12(t) = -5ešt sin (2t) O r2(t) = 5e5t sin (2t)

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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Question
Given the initial value problem
x – 6x1 + x2 = 0
x, – 5x1 – 4x2 = 0
1 (0) — - 2, г2(0) — 0
find #2(t).
%3D
%3D
O r2(t) = 2e5t (cos (2t) + sin (2t))
O r2(t) = e5t (cos (2t) + sin (2t))
O r2(t) = e5t sin (2t)
%3D
O x2(t) = -5e5t sin (2t)
О та (t) — 5еst sin (2t)
Transcribed Image Text:Given the initial value problem x – 6x1 + x2 = 0 x, – 5x1 – 4x2 = 0 1 (0) — - 2, г2(0) — 0 find #2(t). %3D %3D O r2(t) = 2e5t (cos (2t) + sin (2t)) O r2(t) = e5t (cos (2t) + sin (2t)) O r2(t) = e5t sin (2t) %3D O x2(t) = -5e5t sin (2t) О та (t) — 5еst sin (2t)
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