Loading [MathJax]/jax/output/HTML-CSS/jax.js
Skip to main content
Library homepage
 

Text Color

Text Size

 

Margin Size

 

Font Type

Enable Dyslexic Font
Mathematics LibreTexts

11.13: A.12.2- Section 12.2 Answers

( \newcommand{\kernel}{\mathrm{null}\,}\)

1. u(x,t)=43π3n=1(1)n+1(2n1)3sin3(2n1)πtsin(2n1)πx

2. u(x,t)=8π3n=11(2n1)3cos3(2n1)πtsin(2n1)πx

3. u(x,t)=4π3n=1(1+(1)n2)n3cosn7πtsinnπx

4. u(x,t)=83π4n=11(2n1)4sin3(2n1)πtsin(2n1)πx

5. u(x,t)=47π4n=1(1+(1)n2)n4sinn7πtsinnπx

6. u(x,t)=324π3n=1(1)nn3cos8nπt3sinnπx3

7. u(x,t)=96π5n=11(2n1)5cos2(2n1)πtsin(2n1)πx

8. u(x,t)=2432π4n=1(1)nn4sin8nπt3sinnπx3

9. u(x,t)=48π6n=11(2n1)6sin2(2n1)πtsin(2n1)πx

10. u(x,t)=π2cos5tsinx16πn=1n(4n21)2cos2n5tsin2nx

11. u(x,t)=240π5n=11+(1)n2n5cosnπtsinnπx

12. u(x,t)=π25sin5tsinx8pi5n=11(4n21)2sin2n5tsin2nx

13. u(x,t)=240π6n=11+(1)n2n6sinnπtsinnπx

14. u(x,t)=720π5n=1(1)nn5cos2nπtsinnπx

15. u(x,t)=240π6n=1(1)nn6sin3nπtsinnπx

18. u(x,t)=128π3n=1(1)n(2n1)3cos3(2n1)πt4cos(2n1)πx4

19. u(x,t)=64π3n=11(2n1)3[(1)n+3(2n1)π]cos(2n1)πtcos(2n1)πx2

20. u(x,t)=5123π4n=1(1)n(2n1)4sin3(2n1)πt4cos(2n1)πx4

21. u(x,t)=64π4n=11(2n1)4[(1)n+3(2n1)π]sin(2n1)πtcos(2n1)πx2

22. u(x,t)=96π3n=11(2n1)3[(1)n3+4(2n1)π]cos(2n1)5πt2cos(2n1)πx2

23. u(x,t)=96n=11(2n1)3[(1)n+2(2n1)π]cos(2n1)3t2cos(2n1)x2

24. u(x,t)=192π45n=11(2n1)4[(1)n3+4(2n1)π]sin(2n1)5πt2cos(2n1)πx2

25. u(x,t)=1923n=11(2n1)4[(1)n+2(2n1)π]sin(2n1)3t2sin(2n1)x2

26. u(x,t)=384π4n=11(2n1)4[1+(1)n4(2n1)π]cos3(2n1)πt2cos(2n1)πx2

27. u(x,t)=96π3n=11(2n1)3[(1)n5+8(2n1)π]cos(2n1)7πt2cos(2n1)πx2

28. u(x,t)=7683π5n=11(2n1)5[1+(1)n4(2n1)π]sin3(2n1)πt2cos(2n1)πx2

29. u(x,t)=192π47n=11(2n1)4[(1)n5+8(2n1)π]sin(2n1)7πt2cos(2n1)πx2

30. u(x,t)=768π4n=11(2n1)4[1+(1)n2(2n1)π]cos(2n1)πt2cos(2n1)πx2

31. u(x,t)=1536π5n=11(2n1)5[1+(1)n2(2n1)π]sin(2n1)πt2cos(2n1)πx2

32. u(x,t)=12[CMf(x+at)+CMf(xat)]+12ax+atxatCMg(τ)dτ

35. u(x,t)=32πn=11(2n1)3cos4(2n1)tsin(2n1)x2

36. u(x,t)=96π3n=11(2n1)3[1+(1)n4(2n1)π]cos3(2n1)πt2sin(2n1)πx2

37. u(x,t)=8πn=11(2n1)4sin4(2n1)tsin(2n1)x2

38. u(x,t)=64π4n=11(2n1)4[1+(1)n4(2n1)π]sin3(2n1)πt2sin(2n1)πx2

39. u(x,t)=96π3n=11(2n1)3[1+(1)n2(2n1)π]cos3(2n1)πt2sin(2n1)πx2

40. u(x,t)=192πn=1(1)n(2n1)4cos(2n1)3t2sin(2n1)x2

41. u(x,t)=64π4n=11(2n1)4[1+(1)n2(2n1)π]sin3(2n1)πt2sin(2n1)πx2

42. u(x,t)=3843πn=1(1)n(2n1)5sin(2n1)3t2sin(2n1)x2

43. u(x,t)=1536π4n=11(2n1)4[(1)n+3(2n1)π]cos(2n1)5πt2sin(2n1)πx2

44. u(x,t)=384π4n=11(2n1)4[(1)n+4(2n1)π]cos(2n1)πtsin(2n1)πx2

45. u(x,t)=30725π5n=11(2n1)5[(1)n+3(2n1)π]sin(2n1)5πt2sin(2n1)πx2

46. u(x,t)=384π5n=11(2n1)5[(1)n+4(2n1)π]sin(2n1)πtsin(2n1)πx2

47. u(x,t)=12[SMf(x+at)+SMf(xat)]+12ax+atxatSMg(τ)dτ

50. u(x,t)=4768π4n=11(2n1)4cos5(2n1)πt2cos(2n1)πx2

51. u(x,t)=4t15365π5n=11(2n1)5sin5(2n1)πt2cos(2n1)πx2

52. u(x,t)=2π4548n=11+(1)n2n4cos2ntcosnx

53. u(x,t)=75144π4n=1(1)nn4cosn7πtcosnπx

54. u(x,t)=2π4t524n=11+(1)n2n5sin2ntcosnx

55. u(x,t)=7t5144π57n=1(1)nn5sinn7πtcosnπx

56. u(x,t)=π4303n=11n4cos8ntcos2nx

57. u(x,t)=3548π4n=12+(1)nn4cosnπtcosnπx

58. u(x,t)=π4t3038n=11n5sin8ntcos2nx

59. u(x,t)=3t548π5n=12+(1)nn5sinnπtcosnπx

60. u(x,t)=12[Cf(x+at)+Cf(xat)]+12ax+atxatCg(τ)dτ

63. c. u(x,t)=f(x+at)+f(xat)2+12x+atxatg(u)du

64. u(x,t)=x(1+4at

65. u(x,t)=x2+a2t2+t

66. u(x,t)=sin(x+at)

67. u(x,t)=x3+6tx2+3a2t2x+2a2t3

68. u(x,t)=xsinxcosat+atcosxsinat+sinxsinata


This page titled 11.13: A.12.2- Section 12.2 Answers is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by William F. Trench.

Support Center

How can we help?