Why Not A Regular Sturm-Liouville ProblemWhile solving a regular Sturm-Liouville Problem a student found eigenvaluesа.)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 byWhile solving a regular Sturm-Liouville Problem another student foundu„(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 byWhile solving a regular Sturm-Liouville Problem another student foundu„(x) = sin(2„x)for n = 1,2,3, ..., and 0

Since you have posted a question with multiple sub-parts, we will solve the first three subparts for you. To get the remaining sub-parts solved please repost the complete question and mention the sub-parts. a) Consider λnsin1λn=1100. We will check the number of solutions to this equation using the graphs. Zooming in around the origin, From the graph, we see that the intersection of the two curves y=xsin1x and y=1100 has only finite values. i.e. the solutions to the equation λnsin1λn=1100 are finite. But we know that the set of eigenvalues of a regular Sturm-Liouville problem has countably many eigenvalues. Hence, the obtained result is wrong.(b) Given the eigenvalues are λn=n2π and the eigenfunctions are unx=sinλnx3 λ1=π, u1x=sinπx3λ2=4π, u2x=sin4πx3 Let us check the orthogonality, ∫01u1xu2xdx=∫01sinπx3sin4πx3 dx=0.0294≠0 Hence, they are not orthogonal. Therefore, the result is incorrect.(c) Given the eigenvalues are λn=πn and the eigenfunctions are unx=sinλnx. λ1=π, u1x=sinπxλ2=π2, u2x=sin2πx Let us check the orthogonality, ∫01u1xu2xdx=∫01sinπxsin2πx dx=0.30682≠0 Hence, they are not orthogonal. Therefore, the result is incorrect.

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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?

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?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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