# W t c t 2 20 y c 1 e t c 2 t c 3 te t 21 y c 1 t 2 c

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W ( t ) = c t 2 20. y = c 1 e t + c 2 t + c 3 te t 21. y = c 1 t 2 + c 2 t 3 + c 3 ( t + 1) Section 4.2, page 180 1. 2 exp ( i ( 𝜋 4) + 2 m 𝜋 )) 2. 2 exp ( i (2 𝜋 3 + 2 m 𝜋 )) 3. 3 exp ( i ( 𝜋 + 2 m 𝜋 )) 4. 2 exp ( i (11 𝜋 6) + 2 m 𝜋 ) 5. 1 , 1 2 ( 1 + i 3 ) , 1 2 ( 1 i 3 ) 6. 2 1 4 e 𝜋 i 8 , 2 1 4 e 7 𝜋 i 8 7. ( 3 + i ) 2 , ( 3 + i ) 2 8. y = c 1 e t + c 2 te t + c 3 e t 9. y = c 1 e t + c 2 te t + c 3 t 2 e t 10. y = c 1 + c 2 t + c 3 e 2 t + c 4 te 2 t 11. y = c 1 cos t + c 2 sin t + e 3 t 2 ( c 3 cos ( t 2 ) + c 4 sin ( t 2 )) + e 3 t 2 ( c 5 cos ( t 2 ) + c 6 sin ( t 2 )) 12. y = c 1 e t + c 2 te t + c 3 t 2 e t + c 4 e t + c 5 te t + c 6 t 2 e t 13. y = c 1 + c 2 t + c 3 e t + c 4 e t + c 5 cos t + c 6 sin t 14. y = c 1 + c 2 e t + c 3 e 2 t + c 4 cos t + c 5 sin t 15. y = e t (( c 1 + c 2 t ) cos t + ( c 3 + c 4 t ) sin t ) + e t (( c 5 + c 6 t ) cos t + ( c 7 + c 8 t ) sin t ) 16. y = ( c 1 + c 2 t ) cos t + ( c 3 + c 4 t ) sin t 17. y = c 1 e t + c 2 e ( 2 + 2 ) t + c 3 e ( 2 2 ) t 18. y = c 1 e 3 t + c 2 e 2 t + c 3 e ( 3 + 3 ) t + c 4 e ( 3 3 ) t 19. y = c 1 e t 3 + c 2 e t 4 + c 3 e t cos (2 t ) + c 4 e t sin (2 t ) 20. y = 2 2 cos t + sin t

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Boyce 9131 BMAnswersToProblems 2 March 11, 2017 15:55 581 Answers to Problems 581 21. y = 1 2 e t 2 sin ( t 2 ) 1 2 e t 2 sin ( t 2 ) 22. y = 2 t 3 23. y = − 2 3 e t 1 10 e 2 t 1 6 e 2 t 16 15 e t 2 24. y = 2 13 e t + 24 13 e t 2 cos t + 3 13 e t 2 sin t 25. y = 8 18 e t 3 + 8 e t 2 26. y = 95 32 e t + 1 32 e t + 1 2 cos t 17 16 sin t 27. y = 1 2 ( cosh t − cos t ) + 1 2 ( sinh t − sin t ) 28. a. W ( t ) = c , a constant b. W ( t ) = − 8 c. W ( t ) = 4 29. b. u 1 = c 1 cos t + c 2 sin t + c 3 cos ( 6 t ) + c 4 sin ( 6 t ) Section 4.3, page 184 1. y = c 1 e t + c 2 te t + c 3 e t + 1 2 te t + 3 2. y = c 1 e t + c 2 e t + c 3 cos t + c 4 sin t 3 t 1 4 t sin t 3. y = c 1 e t + c 2 cos t + c 3 sin t + 1 2 te t + 4( t 1) 4. y = c 1 + c 2 t + c 3 e 2 t + c 4 e 2 t 1 3 e t 1 48 t 4 1 16 t 2 5. y = c 1 cos t + c 2 sin t + c 3 t cos t + c 4 t sin t + 3 + 1 9 cos 2 t 6. y = c 1 + c 2 t + c 3 t 2 + c 4 e t + e t 2 ( c 5 cos ( 3 t 2 ) + c 6 sin ( 3 t 2 )) + 1 24 t 4 7. y = 3 16 (1 − cos (2 t )) + 1 8 t 2 8. y = ( t 4) cos t ( 3 2 t + 4 ) sin t + 3 t + 4 9. y = − 2 5 cos t 4 5 sin t + 1 20 e t + 81 40 e t + 73 520 e 3 t + 77 65 cos (2 t ) 49 130 sin (2 t ) 10. Y ( t ) = t ( A 0 t 3 + A 1 t 2 + A 2 t + A 3 ) + Bt 2 e t 11. Y ( t ) = t ( A 0 t + A 1 ) e t + B cos t + C sin t 12. Y ( t ) = t ( A 0 t 2 + A 1 t + A 2 ) + ( B 0 t + B 1 ) cos t + ( C 0 t + C 1 ) sin t 13. Y ( t ) = Ae t + ( B 0 t + B 1 ) e t + te t ( C cos t + D sin t ) 14. k 0 = a 0 , k n = a 0 𝛼 n + a 1 𝛼 n 1 + + a n 1 𝛼 + a n Section 4.4, page 188 1. y = c 1 + c 2 cos t + c 3 sin t − ln cos t ( sin t ) ln (sec t + tan t ) 2. y = c 1 + c 2 e t + c 3 e t 1 2 t 2 3. y = c 1 e t + c 2 e t + c 3 e 2 t + 1 30 e 4 t 4. y = c 1 e t + c 2 cos t + c 3 sin t 1 5 e t cos t 5. y = c 1 e t + c 2 cos t + c 3 sin t 1 2 ( cos t ) ln cos t + 1 2 ( sin t ) ln cos t 1 2 t cos t 1 2 t sin t + 1 2 e t t t 0 ( e s ∕ cos s ) ds 6.
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• Spring '16
• Anhaouy
• Districts of Vienna, Boyce, e2t, 3y, = min, + c2 sin x

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