Chapt_10 - Part III Systems of Differential Equations 10 1....

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Part III Systems of Differential Equations 10 10 Systems of Linear Differential Equations EXERCISES 10.1 Preliminary Theory 1. Let X = µ x y . Then X 0 = µ 3 5 48 X . 2. Let X = µ x y . Then X 0 = µ 4 7 50 X . 3. Let X = x y z . Then X 0 = 34 9 6 10 10 4 3 X . 4. Let X = x y z . Then X 0 = 1 2 1 X . 5. Let X = x y z . Then X 0 = 1 11 21 1 111 X + 0 3 t 2 t 2 + t 0 t + 1 0 2 . 6. Let X = x y z . Then X 0 = 34 0 590 016 X + e t sin2 t 4 e t cos2 t e t . 7. dx dt =4 x +2 y + e t ; dy dt = x +3 y e t 8. dx dt =7 x +5 y 9 z 8 e 2 t ; dy dt x + y + z e 5 t ; dz dt = 2 y z + e 5 t 3 e 2 t 9. dx dt = x y z + e t 3 t ; dy dt =3 x 4 y + z e t + t ; dz dt = 2 x y +6 z e t t 10. dx dt x 7 y + 4sin t +( t 4) e 4 t ; dy dt = x + y + 8sin t +(2 t +1) e 4 t 11. Since X 0 = µ 5 10 e 5 t and µ 3 4 4 7 X = µ 5 10 e 5 t 551
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
10.1 Preliminary Theory we see that X 0 = µ 3 4 4 7 X . 12. Since X 0 = µ 5cos t 5sin t 2cos t 4sin t e t and µ 25 24 X = µ t t t t e t we see that X 0 = µ X . 13. Since X 0 = µ 3 2 3 e 3 t/ 2 and µ 1 1 4 1 1 X = µ 3 2 3 e 3 t/ 2 we see that X 0 = µ 11 / 4 1 1 X . 14. Since X 0 = µ 5 1 e t + µ 4 4 te t and µ 21 10 X = µ 5 1 e t + µ 4 4 te t we see that X 0 = µ X . 15. Since X 0 = 0 0 0 and 121 6 1 2 1 X = 0 0 0 we see that X 0 = 6 1 2 1 X . 16. Since X 0 = cos t 1 2 sin t 1 2 cos t cos t sin t and 10 1 11 0 20 1 X = cos t 1 2 sin t 1 2 cos t cos t sin t we see that X 0 = 1 X . 17. Yes, since W ( X 1 , X 2 )= 2 e 8 t 6 = 0 the set X 1 , X 2 is linearly independent on −∞ <t< . 18. Yes, since W ( X 1 , X 2 )=8 e 2 t 6 = 0 the set X 1 , X 2 is linearly independent on −∞ . 19. No, since W ( X 1 , X 2 , X 3 ) = 0 the set X 1 , X 2 , X 3 is linearly dependent on −∞ . 20. Yes, since W ( X 1 , X 2 , X 3 84 e t 6 = 0 the set X 1 , X 2 , X 3 is linearly independent on −∞ . 21. Since X 0 p = µ 2 1 and µ 14 32 X p + µ 2 4 t + µ 7 18 = µ 2 1 552
Background image of page 2
10.1 Preliminary Theory we see that X 0 p = µ 14 32 X p + µ 2 4 t + µ 7 18 . 22. Since X 0 p = µ 0 0 and µ 21 1 1 X p + µ 5 2 = µ 0 0 we see that X 0 p = µ 1 1 X p + µ 5 2 . 23. Since X 0 p = µ 2 0 e t + µ 1 1 te t and µ 34 X p µ 1 7 e t = µ 2 0 e t + µ 1 1 te t we see that X 0 p = µ X p µ 1 7 e t .
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/17/2010 for the course MATHEMATIC MAS201 taught by Professor Xingqin during the Spring '10 term at Korea Advanced Institute of Science and Technology.

Page1 / 53

Chapt_10 - Part III Systems of Differential Equations 10 1....

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online