14.45: Section 9.3 Answers
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1. yp=e−x(2+x−x2)
2. yp=−e−3x4(3−x+x2)
3. yp=ex(1+x−x2)
4. yp=e−2x(1−5x+x2)
5. yp=−xex2(1−x+x2−x3)
6. yp=x2ex(1+x)
7. yp=xe−2x2(2+x)
8. yp=x2ex2(2+x)
9. yp=x2e2x2(1+2x)
10. yp=x2e3x(2+x−x2)
11. yp=x2e4x(2+x)
12. yp=x3ex/248(1+x)
13. yp=e−x(1−2x+x2)
14. yp=e2x(1−x)
15. yp=e−2x(1+x+x2−x3)
16. yp=ex3(1−x)
17. yp=ex(1+x)2
18. yp=xex(1+x3)
19. yp=xex(2+x)
20. yp=xe2x6(1−x2)
21. yp=4xe−x/2(1+x)
22. yp=xex6(1+x2)
23. yp=x2e2x6(1+x+x2)
24. yp=x2e2x6(3+x+x2)
25. yp=x3ex48(2+x)
26. yp=x3ex6(1+x)
27. yp=−x3e−x6(1−x+x2)
28. yp=x3e2x12(2+x−x2)
29. yp=e−x[(1+x)cosx+(2−x)sinx]
30. yp=e−x[(1−x)cos2x+(1+x)sin2x]
31. yp=e2x[(1+x−x2)cosx+(1+2x)sinx]
32. yp=ex2[(1+x)cos2x+(1−x+x2)sin2x]
33. yp=x13(8cos2x+14sin2x)
34. yp=xex[(1+x)cosx+(3+x)sinx]
35. yp=xe2x2[(3−x)cos2x+sin2x]
36. yp=−xe3x12(xcos3x+sin3x)
37. yp=−ex10(cosx+7sinx)
38. yp=ex12(cos2x−sin2x)
39. yp=xe2xcos2x
40. yp=−e−x2[(1+x)cosx+(2−x)sinx]
41. yp=xe−x10(cosx+2sinx)
42. yp=xex4−(3cos2x−sin2x)
43. yp=xe−2x8[(1−x)cos3x+(1+x)sin3x]
44. yp=−xex4(1+x)sin2x
45. yp=x2e−x4(cosx−2sinx)
46. yp=−x2e2x32(cos2x−sin2x)
47. yp=x2e2x8(1+x)sinx
48. yp=2x2ex+xe2x−cosx
49. yp=e2x+xex+2xcosx
50. yp=2x+x2+2xex−3xe−x+4e3x
51. yp=xex(cos2x−2sin2x)+2xe2x+1
52. yp=x2e−2x(1+2x)−cos2x+sin2x
53. yp=2x2(1+x)e−x+xcosx−2sinx
54. yp=2xex+xe2x+cosx
55. yp=xex6(cosx+sin2x)
56. yp=x254[(2+2x)ex+3e−2x]
57. yp=x8sinhxsinx
58. yp=x3(1+x)e−x+xe−2x
59. yp=xex(2x2+cosx+sinx)
60. y=e2x(1+x)+c1e−x+ex(c2+c3x)
61. y=e3x(1−x−x22)+c1ex+e−x(c2cosx+c3sinx)
62. y=xe2x(1+x)2+c1ex+c2e2x+c3e3x
63. y=x2e−x(1−x)2+c1+e−x(c2+c3x)
64. y=x3ex24(4+x)+ex(c1+c2x+c3x2)
65. y=x2e−x16(1+2x−x2)+ex(c1+c2x)+e−x(c3+c4x)
66. y=e−2x[(1+x2)cosx+(32−2x)sinx]+c1ex+c2e−x+c3e−2x
67. y=−xexsin2x+c1+c2ex+ex(c3cosx+c4sinx)
68. y=−x2ex16(1+x)cos2x+ex[(c1+c2x)cos2x+(c3+c4x)sin2x]
69. y=(x2+2)ex−e−2x+e3x
70. y=e−x(1+x+x2)+(1−x)ex
71. y=(x212+16)xe−x/2−ex
72. y=(2−x)(x2+1)e−x+cosx−sinx
73. y=(2−x)cosx−(1−7x)sinx+e−2x
74. 2+ex[(1+x)cosx−sinx−1]