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11.12: A.12.1- Section 12.1 Answers

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8. u(x,t)=8π3n=11(2n1)3e(2n1)2π2tsin(2n1)πx

9. u(x,t)=4πn=11(2n1)e9(2n1)2π2t/16sin(2n1)πx4

10. u(x,t)=π2e3tsinx16πn=1n(4n21)e12n2tsin2nx

11. u(x,t)=32π3n=1(1(1)n2)n3e9n2π2t/4sinnπx2

12. u(x,t)=324π3n=1(1)nn3e4n2π2t/9sinnπx3

13. u(x,t)=8π2n=1(1)n+1(2n1)2e(2n1)2π2tsin(2n1)πx2

14. u(x,t)=720π5=720π5n=1(1)nn5e7n2π2tsinnπx

15. u(x,t)=96π5n=11(2n1)5e5(2n1)2π2tsin(2n1)πx

16. u(x,t)=240π5n=11+(1)n2n5e2n2π2tsinnπx

17. u(x,t)=163+64π2n=1(1)nn2e9π2n2t/16cosnπx4

18. u(x,t)=83+16π2n=11n2en2π2tcosnπx2

19. u(x,t)=161π2n=11n2e36n2π2tcos2nπx

20. u(x,t)=4384π4n=11(2n1)4e3(2n1)2π2t/4cos(2n1)πx2

21. u(x,t)=285576π4n=1(1)nn4e5n2π2t/2cosnπx2

22. u(x,t)=2548π4n=11+(1)n2n4e3n2π2tcosnπx

23. u(x,t)=3548π4n=12+(1)nn4en2π2tcosnπx

24. u(x,t)=π4303n=11n4e4n2tcos2nx

25. u(x,t)=8πn=1(1)n(2n+1)(2n3)e(2n1)2π2t/4sin(2n1)πx2

26. u(x,t)=8n=11(2n1)2[(1)n+4(2n1)π]e3(2n1)2t/4sin(2n1)x2

27. u(x,t)=128π3n=11(2n1)3e5(2n1)2t/16sin(2n1)πx4

28. u(x,t)=96π3n=11(2n1)3[1+(1)n4(2n1)π]e(2n1)2π2t/4sin(2n1)πx2

29. u(x,t)=96π3n=11(2n1)3[1+(1)n2(2n1)π]e(2n1)2π2t/4sin(2n1)πx2

30. u(x,t)=192π4n=1(1)n(2n1)4e(2n1)2π2t/4sin(2n1)πx2

31. u(x,t)=1536π4n=11(2n1)4[(1)n+3(2n1)π]e(2n1)2π2t/4sin(2n1)πx2

32. u(x,t)=384π4n=11(2n1)4[(1)n+4(2n1)π]e(2n1)2π2t/4sin(2n1)πx2

33. u(x,t)=64n=1e3(2n1)2t/4(2n1)3[(1)n+3(2n1)π]cos(2n1)x2

34. u(x,t)=16πn=1(1)n2n1e(2n1)2tcos(2n1)x4

35. u(x,t)=64πn=1(1)n2n1[18(2n1)2π2]e9(2n1)2π2t/64cos(2n1)πx8

36. u(x,t)=8π2n=11(2n1)2e3(2n1)2π2t/4cos(2n1)πx2

37. u(x,t)=96π3n=11(2n1)3[(1)n+2(2n1)π]e(2n1)2π2t/4cos(2n1)πx2

38. u(x,t)=32πn=1(1)n(2n1)3e7(2n1)2t/4cos(2n1)x2

39. u(x,t)=96π3n=11(2n1)3[(1)n5+8(2n1)π]e(2n1)2π2t/4cos(2n1)πx2

40. u(x,t)=96π3n=11(2n1)3[(1)n3+4(2n1)π]e(2n1)2π2t/4cos(2n1)πx2

41. u(x,t)=768π4n=11(2n1)4[1+(1)n2(2n1)π]e(2n1)2π2t/4cos(2n1)πx2

42. u(x,t)=384π4n=11(2n1)4[1+(1)n4(2n1)π]e(2n1)2π2t/4cos(2n1)πx2

43. u(x,t)=122πn=1(1)n2n1e(2n1)2π2a2t/L2cos(2n1)πxL

44. u(x,t)=2πn=11n[1cosnπ2]en2π2a2t/L2sinnπxL

45. u(x,t)=4πn=112n1sin(2n1)π4e(2n1)2π2a2t/4L2cos(2n1)πx2L

46. u(x,t)=4πn=112n1[1cos(2n1)π4]e(2n1)2π2a2t/4L2sin(2n1)πx2L

48. u(x,t)=1x+x3+4πn=1e9π2(2n1)2t/16(2n1)sin(2n1)πx4

49. u(x,t)=1+x+x28π3n=1e(2n1)2π2t(2n1)3sin(2n1)πx

50. u(x,t)=1x+x3+8π2n=11(2n1)2e3(2n1)2π2t/4cos(2n1)πx2

51. u(x,t)=x2x264πn=1(1)n2n1[18(2n1)2π2]e9(2n1)2π2t/64cos(2n1)πx8

52. u(x,t)=sinπx+8πn=1(1)n(2n+1)(2n3)e(2n1)2π2t/4sin(2n1)πx2

53. u(x,t)=x3x+3+32π3n=1e(2n1)2π2t/4(2n1)3sin(2n1)πx2


This page titled 11.12: A.12.1- Section 12.1 Answers is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by William F. Trench.

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