11.17: A.13.2- Section 13.2 Answers
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1. (ebxy′)′+cebxy=0
2. (xy′)′+(x−ν2x)y=0
3. (√1−x2y′)′+α2√1−x2y=0
4. (xby′)′+cxb−2y=0
5. (e−x2y′)′+2αe−x2y=0
6. (xe−xy′)′+αe−xy=0
7. ((1−x2)y′)′+α(α+1)y=0
9. λn=n2π2,yn=e−xsinnπx(n= positive integer)
10. λ0=−1,y0=1λn=n2π2,yn=e−x(nπcosnπx+sinnπx)(n= positive integer)
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21. λ=0,y=xe−x20.1907286,118.8998692,296.5544121,553.1646458y=e−xsin√λx
22. λn=n2π2,yn=xsinnπ(x−2)(n= positive integer)
23. λ=0,y=x(2−x)20.1907286,118.8998692,296.5544121553.1646458,y=xsin√λ(x−2)
24. 3.3730893,23.1923372,62.6797232,121.8999231,200.8578309y=xsin√λ(x−1)
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26. λ0=−1α2y0=e−x/aλn=n2,yn=nαcosnx−sinnx,n=1,2,…
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29. b. λ=−α2/β2y=e−αx/β