Page 364 - Schaum's Outline of Differential Equations

ANSWERS TO SUPPLEMENTARY PROBLEMS 347

4)
4)
10.44. / - 4y'" + 85y" = 0 10.45. / - 8/" + 186y" - 680);' + 7225y = 0
x
5)
x
3
x
2
4)
10.46. / - 5/ - 50y + 250y" + 625y' -3125y = 0 10.47. y = cie~ + c 2xe~ + C 3x e~ + c 4x e~ x
(3)
10.48. y = Ci cos 4x + c 2 sin 4x + c 3 cos 3x + c 4 sin 3x 10.49. y = Ci cos 4x + c 2 sin 4x + c 3x cos 4x + c 4x sin 4x
10.50. y = c^ + c^xe * + C 3e + C 4xe 5x
5x
2
CHAPTER 11
2
11.15. y p = A 1x + A 0 11.16. y p = A 2x + A 1x + A 0
2
11.17. y p = A 2x + A 1x + A 0 11.18. y p = Ae- 2x
2 1
11.19. y p = Ae 5x 11.20. y p = Axe -
11.21. y p = A sin 3x + B cos 3x 11.22. y p = A sin 3;t + B cos 3;t

11.23. y p = (AiX + A 0) sin 3x + (B^ + B 0) cos 3x 11.24. y p = Ajjc + A 0 + Se &

5
3
11.25. y p = (AJ* + A 0)e -* 11.26. ^ = XA^ + A 0)e ^
3 1
11.27. y p = Ae - 11.28. ^ = (A^ + A 0)e ^
3
5 1
5 1
11.29. y p = Ae - 11.30. y p = (A 2^ + A!* + A 0)e -
2
11.31. v, = Asimj2x +Bcos^x 11.32. ^^(Aj^ +A^ +A 0 )sin>/2^
2
+ (S 2^ + Sjjc + S 0)cos>/2.
11.33. y n = A sin 3x + B cos 3x 11.34. y p = A sin 4x + B cos 4x + C sin 7x + D cos 7jc

x
11.35. y p = Ae x sin 3x + Be cos 3x 11.36. ;y p = ^(Ae sin 3x + Be cos 3;c)
&
5x
11.37. jtp = i(Aji + A 0 ) 11.38. x p = t(A 2t 2 + Ajf + A 0)
11.39. x p = (Ait + A 0)e- ' 2 + Bt 11.40. x p = t\Ae<)

2
11.41. x p = t (Ait + A 0)e' 11.42. x p = At + (Bit + B 0) sin t + (Ctf + C 0) cos t
x
2
2
x
11.43. Xp=(A 1t + A <>)e 'sm3t 11.44. y = c- le + c?xe + x + 4x +5
2
+ (BJ + S 0)e ' cos3t
1
11.45. y = Cje* + Cj^e + Se 21 11.46. y = c^ + c 2xe — 2 sin x
x
x
2x
2x
x
11.49. y = c- le + xe x 11.50. y = c,e + xe -e -l