Page 363 - Schaum's Outline of Differential Equations

346 ANSWERS TO SUPPLEMENTARY PROBLEMS

9.34. u = c,e'cosj3t + c 2e'sm\/3t

(2
9.35. u = c ie (2+ ^'+c 2e -^' 9.36. u = c l + c 2e '
36
6
6
9.37. u = Cje ' + c 2e~ ' = ki cosh 6t + k 2 sin 6t
7
2
7
9
9
9.39. Q = c^ ^" + c/ -^" 2 9.40. P = Cje ' + c 2te '
3
9.42. N = c^ * + c 2e- Sx
lse
9.44. T = c 1e- + c 26e- lse
9.45. ;. R = CI + c 2e- se

CHAPTER 10

x
1
x
10.16. y = cie~ + c 2e* + c^e * 10.17. y = c 1e + c 2xe* + c 3g-*
x
x
10.18. y = c 1e + c^e* + CjxV 10.19. y = c 1e + c 2 cos x + c 3 sin x
10.20. y = (ci + c 2x) cos x + (c 3 + c 4x) sin x 10.21. y = c^e* + c 2e~ + c 3 cos x + c 4 sin x
x
2j:
x
2
2x
x
x
10.22. y = c le + c 2e~ + c ?lxe~ + c^e~ x 10.23. y = c^ * + c 2xe' + c^ cos 2x + C 4e sin 2x
10.24. y = c 1 + c 2x + c-jX 2 + c 4e~ 5x
2
10.26. y = c^e * cos 2x + c^ sin 2x + c 3e~ 2j: 10.27.. x = c 1e ' + c 2te '+C 3t e '+ c 4fe '
2
2x
+ c 4xe~ + c^ + c 6e~ x
10.28. x = c 1 + c 2t + c 3t 2 10.29. x = c 1 cos t + c 2 sin t + c 3 cos 3t + c 4 sin 3t

x
1
10.30. x = c^ ' + c 2 cos 5t + c 3 s'mSt 10.31. q = qe + c 2e~ + c 3 cos^/2x + c 4 sin\/2x
5
x
x
6x
10.32. q = cf* + c 2e~ + c 3e^ + c 4e^ x 10.33. N = c 1e- + c 2e + c 3e 10x
8x
fl
lx
10.34. r = Cle- + c^ + c 30V« + c 4<?V + c 50V« 10.35. y = c le + c 2e* + c 3e- Ux
e
x
2j:
2x
10.36. y = c l + c 2 cos 19x + c 3 sin 19x 10.37. y = c 1 + c 2x + C 3e cos 9x + C 4e sin 9x
5x
10.38. y = c^ cos 9x + c 2e^ sin 9x 10.39. y = c^ + C 2xe + c^e^ + c 4e~ 5x
2x
2x
+ C 3xe cos 9x + C 4xe sin 9x + c<xe- 5x
10.40. y = Ci cos 6x + c 2 sin 6x + c 3x cos 6x 10.41. y = e~ '(CjCos^; + c 2 sinjc + c 3xcosx
3
3x
2
+ c 4x sin 6x + c^ cos 6x + c 6x sin 6x + c 4xsinx) + e (c 5cosx + c 6 sinjc
+ CjXcosx + CgXs'mx)
10.42. y'" + 4y" - 124y' + 224y = 0 10.43. /" + 361/ = 0