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Mathematics LibreTexts

11.17: A.13.2- Section 13.2 Answers

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

1. (ebxy)+cebxy=0

2. (xy)+(xν2x)y=0

3. (1x2y)+α21x2y=0

4. (xby)+cxb2y=0

5. (ex2y)+2αex2y=0

6. (xexy)+αexy=0

7. ((1x2)y)+α(α+1)y=0

9. λn=n2π2,yn=exsinnπx(n= positive integer)

10. λ0=1,y0=1λn=n2π2,yn=ex(nπcosnπx+sinnπx)(n= positive integer)

11.

  1. λ=0 is an eigenvalue y0=2x
  2. none
  3. 5.0476821,14.9198790,29.7249673,49.4644528y=2λcosλxsinλx

12.

  1. λ=0 isn't an eigenvalue
  2. 0.5955245y=coshλx
  3. 8.8511386,38.4741053,87.8245457,156.9126094y=cosλx

13.

  1. λ=0 isn't an eigenvalue
  2. none
  3. 0.1470328,1.4852833,4.5761411,9.6059439y=λcosλx+sinλx

14.

  1. λ=0 isn't an eigenvalue
  2. 0.1945921y=2λcoshλxsinhλx
  3. 1.9323619,5.9318981,11.9317920,19.9317507y=2λcosλxsinλx

15.

  1. λ=0 isn't an eigenvalue
  2. 1.0664054y=coshλx
  3. 1.5113188,8.8785880,21.2104662,38.4805610y=cosλx

16.

  1. λ=0 isn't an eigenvalue
  2. 1.0239346y=λcoshλxsinhλx
  3. 2.0565705,9.3927144,21.7169130,38.9842177y=λcosλxsinλx

17.

  1. λ=0 isn't an eigenvalue
  2. 0.4357577y=2λcoshλxsinhλx
  3. 0.3171423,3.7055350,9.1970150,16.8760401y=2λcosλxsinλx

18.

  1. λ=0 isn't an eigenvalue
  2. 2.1790546,9.0006633y=λcoshλx3sinhλx
  3. 5.8453181,17.9260967,35.1038567,57.2659330y=λcosλx3sinλx

19.

  1. λ=0 is an eigenvalue y0=2x
  2. 1.0273046y=2λcoshλxsinhλx
  3. 8.8694608,16.5459202,26.4155505,38.4784094y=2λcosλxsinλx

20.

  1. λ=0 isn't an eigenvalue
  2. 7.9394171,3.1542806y=2λcoshλx5sinhλx
  3. 29.3617465,78.777456,147.8866417,236.7229622y=2λcosλx5sinλx

21. λ=0,y=xex20.1907286,118.8998692,296.5544121,553.1646458y=exsinλx

22. λn=n2π2,yn=xsinnπ(x2)(n= positive integer)

23. λ=0,y=x(2x)20.1907286,118.8998692,296.5544121553.1646458,y=xsinλ(x2)

24. 3.3730893,23.1923372,62.6797232,121.8999231,200.8578309y=xsinλ(x1)

25.

  1. L<δ<0
  2. δ=L

26. λ0=1α2y0=ex/aλn=n2,yn=nαcosnxsinnx,n=1,2,

27.

  1. y=xα
  2. y=αkcoshkxsinkx
  3. y=αkcoskxsinkx

29. b. λ=α2/β2y=eαx/β


This page titled 11.17: A.13.2- Section 13.2 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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