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Problem #7: Consider y" + ly = 0, subject to the periodic boundary conditions y(-1/2) = y(1/2), y'(-1/2) = y'(7/2). Which of the following is a set of eigenfunctions for this boundary value problem? (A) (1, cos mx, cos 27x, (©) {1, cos £.xcos 4 x, (E) {1, coszx, coszx, (G) {1, cos 2x, cos 2 x, , sin ax, sin 2.1x, sin 3AX, ...} B) {1, cos2x, cos x, ... , sin 2x, sin x, sin ex, ...} sin...
Problem #8: Find the eigenfunctions for the following boundary value problem. x2y"-19xy(100 A)y = 0. y(e) = 0, y(1) = 0. In the eigenfunction take the arbitrary constant (either c1 or c) from the general solution to be 1 Enter your answer as a symbolic function of x.n, as in these examples Problem #8: Do not include 'yin your answer. Problem #8: Find the eigenfunctions for the following boundary value problem. x2y"-19xy(100 A)y = 0. y(e) = 0, y(1) =...
2. Determine the normalized eigenfunctions of the given problem y" + ly = 0, y(0) = 0, y'(1)=0)
Problem 11. 12 marks] Consider the following two-point boundary value problem: y" + y' + ßy = 0, y(0) = 0, y(1) = 0, where ß is a real nurnber. we know the problern has a trivial solution, i.e. y(x) = 0, Discuss how the value of B influences the nontrivial solutions of the boundary value problem, and get the nontrivial solutions (Find all the real eigenvalues β and the corresponding eigenfunctions.) Problem 11. 12 marks] Consider the following two-point...
(1 point) Determine the values of (eigenvalues) for which the boundary-value problem g” + y = 0, 0 < x < 4 y(0) = 0, y' (4) = 0 has a non-trivial solution. An = a , n=1,2,3,... Your formula should give the eigenvalues in increasing order. The eigenfunctions to the eigenvalue in are Yn = Cn* sin(n*pi/2*x) where On is an arbitrary constant.
Just solve it without plotting Solve the eigen value problem problem x2y" + xy' + ly = 0 On boundary conditions y(1) = 0 and y(5) = 0. a) Find the eigen values and eigen functions b) Using the eigen functions, expand the following function -1, 1<x<3 f(x) = { 1, 3<x< 5 into a series of Eigenfunctions and plot the result using n = 5, 10, 25, 100 terms to examine the convergence of series.
Problem #8: Find the eigenfunctions for the following boundary value problem In the eigenfunction take the arbitrary constant (either ci or c2) from the general solution to be 1 Enter your answer as a symbolic function of x,n, as in these examples Do not include 'y-'in your answer. Problem #8 Problem #8: Find the eigenfunctions for the following boundary value problem In the eigenfunction take the arbitrary constant (either ci or c2) from the general solution to be 1 Enter...
- Consider the following boundary value problem, x?y" + 3xy' + (1+2) y = 0, y1) = 0, yle) = 0 (a) Find the eigenvalues. (b) Find the eigenfunctions. Take the arbitrary constant (either C1 or c2) from the general solution to be 1.
Consider the following boundary value problem, x?y"' + 13xy' + (36+2) y = 0, y(1) = 0, yler/8 ) = 0 (a) Find the eigenvalues. (b) Find the eigenfunctions. Take the arbitrary constant (either cı or c2) from the general solution to be 1.
Consider the following boundary value problem, y" +(+5) y = 0, y'() = 0, y(9) = 0 (a) Find the eigenvalues. (b) Find the eigenfunctions. Take the arbitrary constant (either cu or c) from the general solution to be 1. Consider the following boundary value problem, y" + (8 + 5) y = 0, y'(o) = 0, 9) = 0 (a) Find the eigenvalues. (b) Find the eigenfunctions. Take the arbitrary constant (either cy or c2) from the general solution...