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Find the general solution of the system of equations x' = (² ) x + ( 9 -82 -9 cos t sin t x = Choose one Choose one G₂ (1 CL • sint) + c₂ (² 9 sint + cost sin t st) + ²2 ( 1 ) + cost-1/2 ( 8 ) t sint a(² (9 cost-sint) + c₂ (² 9 sin ( + cost sint ¹) + ( 2 ) t cost-/ ( 8 ) t sint (2) cost-(33) sint 19 cost-sint) + ca (1 (³ 9 sini + cost - sin ost) + 2 ( 2 ) t cost-½ (3) tsint-(2) cost-( 83 ) sint 9 83 9 cost-sint cont ²² ) + ₁₂ (² 9 sint + cost sin t st) - 2 ( 2 ) t cost + (3) tsint-(2) cost-(33) sint ½ 5₂(8 ^²)+ ₁₂ (² 9 sin ( + cost sin t st) - ( 2 ) cost - (83) sint 9 CL 9 cost-sint cont 9 cost-sint cont

Find the general solution of the system of equations x' = (² ) x + ( 9 -82 -9 cos t sin t x = Choose one Choose one G₂ (1 CL • sint) + c₂ (² 9 sint + cost sin t st) + ²2 ( 1 ) + cost-1/2 ( 8 ) t sint a(² (9 cost-sint) + c₂ (² 9 sin ( + cost sint ¹) + ( 2 ) t cost-/ ( 8 ) t sint (2) cost-(33) sint 19 cost-sint) + ca (1 (³ 9 sini + cost - sin ost) + 2 ( 2 ) t cost-½ (3) tsint-(2) cost-( 83 ) sint 9 83 9 cost-sint cont ²² ) + ₁₂ (² 9 sint + cost sin t st) - 2 ( 2 ) t cost + (3) tsint-(2) cost-(33) sint ½ 5₂(8 ^²)+ ₁₂ (² 9 sin ( + cost sin t st) - ( 2 ) cost - (83) sint 9 CL 9 cost-sint cont 9 cost-sint cont

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 9 x' = - (1 -32)x+ ( cos t sin t *). -9 x = Choose one Choose one 9 (³ ²² ) + c₂ ( st) + 2/(?) t cost-1/2 ( 8 ) t sint 9 sint + cost sin t 9 sint + cost 9 9 st) + ²2 ( 1 ) t cost-½ (2) tsint - (2) sin t 0 9 sint + cost 1 ost) + ²2 ( 2 ) t cost - ( 8 ) t sint - ¼ - sint 9 sint + cost sin t st) - 2 ( 2 ) t cost + 2 ( 8 ) tsint 9 sint + cost sin t C1 2(90 9 cost - sint cost 9 cost - sint - cos t 9 cost - sint cost a(² a(² 9 cost - sint Cost it). int). ¹t). C₂ (8 C1 + C₂ + C₂ + C₂ 9 cost-sint Cost nt) + c₂ ( 83 -1 (8³) s 9 83 ( 8³ ) s 9 83 ( 33 ) sint 9 cost- ( 2 ) cost - ( 2 ) cost - cost)-(2) cost-1(83) sint 9 sin t sin t
Transcribed Image Text:Find the general solution of the system of equations 9 x' = - (1 -32)x+ ( cos t sin t *). -9 x = Choose one Choose one 9 (³ ²² ) + c₂ ( st) + 2/(?) t cost-1/2 ( 8 ) t sint 9 sint + cost sin t 9 sint + cost 9 9 st) + ²2 ( 1 ) t cost-½ (2) tsint - (2) sin t 0 9 sint + cost 1 ost) + ²2 ( 2 ) t cost - ( 8 ) t sint - ¼ - sint 9 sint + cost sin t st) - 2 ( 2 ) t cost + 2 ( 8 ) tsint 9 sint + cost sin t C1 2(90 9 cost - sint cost 9 cost - sint - cos t 9 cost - sint cost a(² a(² 9 cost - sint Cost it). int). ¹t). C₂ (8 C1 + C₂ + C₂ + C₂ 9 cost-sint Cost nt) + c₂ ( 83 -1 (8³) s 9 83 ( 8³ ) s 9 83 ( 33 ) sint 9 cost- ( 2 ) cost - ( 2 ) cost - cost)-(2) cost-1(83) sint 9 sin t sin t
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