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116 Find the general solution to the system x'=Ax where A is the given matrix. 1 -4 474 A= 5 3 5₁0 | | | 2 a) Ox(t)= C, e cos(4 t) b) Ox(t)= Cecos(4t) ce cost -2 1-31- 5 cos(t) d) Ox(t)= Ce cos(4t) 5 1-³1- -2 + sin(4 t) -2 e) Ox(1) Cecos(4 t) 0 | || + ₂ 4 f) O None of the above. -2 -4t |-|-|-|||||||| c) Ox(t)= Ce · |· || + 0,₂0² | COR(E) | | + sin(1) | ~²³ ]]) sin (t) cos(t) 0 5 4 4 [11] | | + + C, e cos(4 t) 0 sin (4 t) 4 | || | || cos(4 t) sin( sin (4 t) 0 | |-2014 -2 5 sin (4 t) - sin (4 t) + sin(4 t) 4 -2 73³0 5 -2 0 2 | 3 || + ₂ ² [CORAD | 3³ | + [:D cos(4 t) + sin(4t) 5 | 2² | + 0,₂ ² (COR41 | 2² | + m (41) | ~ ³ )) t) sin(4 t) 5

116 Find the general solution to the system x'=Ax where A is the given matrix. 1 -4 474 A= 5 3 5₁0 | | | 2 a) Ox(t)= C, e cos(4 t) b) Ox(t)= Cecos(4t) ce cost -2 1-31- 5 cos(t) d) Ox(t)= Ce cos(4t) 5 1-³1- -2 + sin(4 t) -2 e) Ox(1) Cecos(4 t) 0 | || + ₂ 4 f) O None of the above. -2 -4t |-|-|-|||||||| c) Ox(t)= Ce · |· || + 0,₂0² | COR(E) | | + sin(1) | ~²³ ]]) sin (t) cos(t) 0 5 4 4 [11] | | + + C, e cos(4 t) 0 sin (4 t) 4 | || | || cos(4 t) sin( sin (4 t) 0 | |-2014 -2 5 sin (4 t) - sin (4 t) + sin(4 t) 4 -2 73³0 5 -2 0 2 | 3 || + ₂ ² [CORAD | 3³ | + [:D cos(4 t) + sin(4t) 5 | 2² | + 0,₂ ² (COR41 | 2² | + m (41) | ~ ³ )) t) sin(4 t) 5

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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116 Find the general solution to the system x'=Ax where A is the given matrix. 1 -4 44-733 A= 5 50 [0|||||||||| + a) Ox(t)= Ce cos(4 t) b) Ox(t)= Ce cos(4 t) cos(t) 2 -2 1-31- 5 d) Ox(t)= Ce cos(4t) + sin(4 t) -2 5 -2 sin (4 t) 4 -4t |-|-|-|||||||| c) Ox(t)= C₁e²² | | || + C₂0²¹ (COME) | sin (t) cos(t) 0 - 4 cos(4 t) 4 4 -2 [1] | | + 7330 + C, e cos(4 t) + sin(4 t) 0 5 - sin (4 t) sin( sin (4 t) 4 -2 | + sin(1) | 23 | 5 -2 0 2 | 3 || + ₂ ² [COR41 | 3³ | + [:D cos(4 t) + sin(4t) 5 +) | |-2014 0 | [ ² ] + 0,₂6² (cos(41) | 2 | + m (41) | ~ 3]) Ox(t)= Cecos(4 t) -2 5 sin (4 t) t) sin(4 t) 5 f) O None of the above.
Transcribed Image Text:116 Find the general solution to the system x'=Ax where A is the given matrix. 1 -4 44-733 A= 5 50 [0|||||||||| + a) Ox(t)= Ce cos(4 t) b) Ox(t)= Ce cos(4 t) cos(t) 2 -2 1-31- 5 d) Ox(t)= Ce cos(4t) + sin(4 t) -2 5 -2 sin (4 t) 4 -4t |-|-|-|||||||| c) Ox(t)= C₁e²² | | || + C₂0²¹ (COME) | sin (t) cos(t) 0 - 4 cos(4 t) 4 4 -2 [1] | | + 7330 + C, e cos(4 t) + sin(4 t) 0 5 - sin (4 t) sin( sin (4 t) 4 -2 | + sin(1) | 23 | 5 -2 0 2 | 3 || + ₂ ² [COR41 | 3³ | + [:D cos(4 t) + sin(4t) 5 +) | |-2014 0 | [ ² ] + 0,₂6² (cos(41) | 2 | + m (41) | ~ 3]) Ox(t)= Cecos(4 t) -2 5 sin (4 t) t) sin(4 t) 5 f) O None of the above.
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