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Find the general solution of the system of equations 2 -5 x' 0 = - ( ² = ₂ ) x + ( cost), 0 < t < *. π. 1 -2

Find the general solution of the system of equations 2 -5 x' 0 = - ( ² = ₂ ) x + ( cost), 0 < t < *. π. 1 -2

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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Find the general solution of the system of equations 2 -5 x' = (₁ (²=5 ) x-(cost), + 0< 0 < t < T. 1 -2 x = Choose one ▼
Transcribed Image Text:Find the general solution of the system of equations 2 -5 x' = (₁ (²=5 ) x-(cost), + 0< 0 < t < T. 1 -2 x = Choose one ▼
X= Choose one ¹(² 2 cost - sint cos t +0₂ 2 ( 2 sint + cost sin t 1 5 - (2) esint +1 (1) sint 2 cost+aint) +0₂ (2 sint cost) + (1) cos + C₁1 t t sin 1 2 1 5 - (²) raint - ( ₂ ) oct +1 (1) sint 5 2 ( 5 cos 2 cost + sint at) +ex 5 sin t - cost + 2 sin t ) - Asin & (5/2) +t ++ cst (1/2) - sint (1/2) + 1 C₁ (² C1 2 cost - sint cos t 2 sint cos t sin t st) + ²/ ( i ) + cou t t 2 2 -1 (7) tsint-2(1) cost 0₁ (² 2 cost - sint cos t C1 nt)+(² 2 sint + cost sin t * ) + 1/2 ( i ) : cost 1 2 1 5 - (3) tsint-(2) cost 2 5 4 C1 C1 nt) + ₂( 2( *) + 1/ ( i ) : cout t 2
Transcribed Image Text:X= Choose one ¹(² 2 cost - sint cos t +0₂ 2 ( 2 sint + cost sin t 1 5 - (2) esint +1 (1) sint 2 cost+aint) +0₂ (2 sint cost) + (1) cos + C₁1 t t sin 1 2 1 5 - (²) raint - ( ₂ ) oct +1 (1) sint 5 2 ( 5 cos 2 cost + sint at) +ex 5 sin t - cost + 2 sin t ) - Asin & (5/2) +t ++ cst (1/2) - sint (1/2) + 1 C₁ (² C1 2 cost - sint cos t 2 sint cos t sin t st) + ²/ ( i ) + cou t t 2 2 -1 (7) tsint-2(1) cost 0₁ (² 2 cost - sint cos t C1 nt)+(² 2 sint + cost sin t * ) + 1/2 ( i ) : cost 1 2 1 5 - (3) tsint-(2) cost 2 5 4 C1 C1 nt) + ₂( 2( *) + 1/ ( i ) : cout t 2
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