Solve the eigenvalue problems:Ly₁²y = xydr²for the two following sets of boundary conditionsi. y(0)) = 0 and y(3) = 0Ak =Yk (x)ii. y(0)) = 0 and y' (3) = 0Ak =Yk (x)**NOTE: you must leave your answers for the eigenfunctions written in terms of X₁, rather than writing them out explicitly in terms of k, otherwisethey won't be recognised as correct***

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Answered: Solve the eigenvalue problems: Ly - ²y…

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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9 - The eigenvalues An and the eigenfunctions yn for the equation y" + Ay = 0 for the boundary conditions y(0) = 0, y(3) =0 are a) O An NTL , Yn = sin 9. n = 1, 2, 3, ... 3. b) NTL , Yn = sin V3 3 ,n= 1, 2, 3, ... c) , Yn = sin(3nTI), n = 1, 2, 3, ... 3. n2 n2 , Yn = sin(2NAI), n= 1, 2, 3,... d) e) An = n² n², Yn = sin(nTr), n = 1, 2, 3, . .. Boş bırak
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5. The eigenvalues and eigenfunctions of the harmonic problem y" + Ay = 0, 0
Find the eigenvalues and eigenfunctions for the differential operator L(y) = -y" with boundary conditions y' (0) = 0 and y(3) = 0, which is equivalent to the following BVP y" + xy = 0, y' (0) = 0, y(3) = 0. (a) Find all eigenvalues ,, as function of a positive integer n > 1. An = Σ (b) Find the eigenfunctions yn corresponding to the eigenvalues A₁, found in part (a). Yn (x) = Σ
1. Find all eigenvalues An and corresponding eigenfunctions yn to the boundary value problem: y" + xy = 0 y'(0) = 0, y(5) = 0.
3. Determine a general solution to the Cauchy-Euler equation z'y" (x) – 2y(x) = 3z² – 1, z> 0. Usboe A
3. Consider the eigenvalue/boundary value problem for y(t): − 3y" + xy = 0, y′(0) = 0, y' (√3)= 0 (a) Is A = 0 an eigenvalue? If it is, calculate the corresponding eigenfunctions. (b) Determine all negative eigenvalues, A< 0, and calculate the corresponding eigenfunc- tions. Clearly show the calculations and state the reasoning justifying your conclusions.
1. Suppose that An is an eigenvalue with eigenfunction yn of y"+y=0, 0
Consider this differential equation and associated boundary conditions:

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Solve the eigenvalue problems: Ly - ²y = xy for the two following sets of boundary conditions i. y(0)) = 0 and y(3) = 0 == Xk = Yk (x)= ii. y(0)) = 0 and y' (3) = 0 Xk = Yk (x)