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...
please solve all 3 Differential Equation problems 3.8.7 Question Help Consider the following eigenvalue problem for which all of its eigenvalues are nonnegative y',thy-0; y(0)-0, y(1) + y'(1)-0 (a) Show that λ =0 is not an eigenvalue (b) Show that the eigenfunctions are the functions {sin α11,o, where αη įs the nth positive root of the equation tan z -z (c) Draw a sketch indicating the roots as the points of intersection of the curves y tan z and y...
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...
Consider the following boundary value problem, x2y′′ + 17xy′ + (64 + λ) y = 0, y(1) = 0, y(e6 ) = 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, xy" + 17xy' + (64 + 2) y = 0, y(1) = 0, yle) = 0 (a) Find the eigenvalues. (b) Find the eigenfunctions. Take the arbitrary constant (either...
Problem #30: Consider the following boundary value problem, [4 marks] x?y" + 21xy' + (100 + 2)y = 0, y(t) = 0, ye?) = 0 (a) Find the eigenvalues. (b) Find the eigenfunctions. Take the arbitrary constant (either or c) from the general solution to be 1.
Consider the following boundary value problem, x?y" + 13xy' + (36+1) y = 0, y(1) = 0, yle1/3) = 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, 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, r?y" + 19xy' + (81 +2) y = 0, y(1) = 0, y(e) = 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, 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.
(1 point) Determine the values of a (eigenvalues) for which the boundary-value problem y + y = 0, 0 < x < 8 y(0) = 0, y'(8) = 0 has a non-trivial solution. = an ((2n-1)^2pi^2)/256 ,n= 1, 2, 3, ... Your formula should give the eigenvalues in increasing order. The eigenfunctions to the eigenvalue an are Yn = Cn* sin ((2n-1) pi n/16) where Cn is an arbitrary cons
(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.