While solving a regular Sturm-Liouville Problem a student found eigenvalues 2, satisfying the equation 1002, sin(1/2,) = 1. What is wrong with this result? While solving a regular Sturm-Liouville Problem another student found eigenvalues given by 2, = n²n and corresponding eigenfunctions given by un(x) = sin(2„x³) for n = 1,2,3, ..., and 0 < x < 1. What is wrong with this result? While solving a regular Sturm-Liouville Problem another student found eigenvalues given by 2, = 1 n and corresponding eigenfunctions given by u„(x) = sin(2,x) for n 1,2,3, ..., and 0 < x < 1. What is wrong with this result?

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Chapter2: Second-order Linear Odes
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Why Not A Regular Sturm-Liouville Problem
While solving a regular Sturm-Liouville Problem a student found eigenvalues
а.)
2, satisfying the equation 1002, sin(1/2,,) = 1. What is wrong with this result?
b.)
eigenvalues given by 2, = n²n and corresponding eigenfunctions given by
While solving a regular Sturm-Liouville Problem another student found
u„(x) = sin(2„x³)
for n = 1,2,3,..., and 0 < x < 1. What is wrong with this result?
с.)
eigenvalues given by 2, = n Jn and corresponding eigenfunctions given by
While solving a regular Sturm-Liouville Problem another student found
u„(x) = sin(2„x)
for n = 1,2,3, ..., and 0 <x < 1. What is wrong with this result?
d.)
eigenvalues 2, to satisfy the equation A, sin(1/2,) = cos(1/2,). What is wrong with this
result?
While solving a regular Sturm-Liouville Problem another student found
While solving a Regular Sturm-Liouville Problem on the interval 0 < x < 1, a
e.)
student claims to have determined 2, = n for the eigenvalues, with corresponding
eigenfunctions
P„(x) = sin?(nrx)
%3D
for n = 1,2,3,.... Explain why the student must be mistaken.
Transcribed Image Text:Why Not A Regular Sturm-Liouville Problem While solving a regular Sturm-Liouville Problem a student found eigenvalues а.) 2, satisfying the equation 1002, sin(1/2,,) = 1. What is wrong with this result? b.) eigenvalues given by 2, = n²n and corresponding eigenfunctions given by While solving a regular Sturm-Liouville Problem another student found u„(x) = sin(2„x³) for n = 1,2,3,..., and 0 < x < 1. What is wrong with this result? с.) eigenvalues given by 2, = n Jn and corresponding eigenfunctions given by While solving a regular Sturm-Liouville Problem another student found u„(x) = sin(2„x) for n = 1,2,3, ..., and 0 <x < 1. What is wrong with this result? d.) eigenvalues 2, to satisfy the equation A, sin(1/2,) = cos(1/2,). What is wrong with this result? While solving a regular Sturm-Liouville Problem another student found While solving a Regular Sturm-Liouville Problem on the interval 0 < x < 1, a e.) student claims to have determined 2, = n for the eigenvalues, with corresponding eigenfunctions P„(x) = sin?(nrx) %3D for n = 1,2,3,.... Explain why the student must be mistaken.
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