Question

In: Advanced Math

Find the eigenvalues λn and eigenfunctions yn(x) for the given boundary-value problem. (Give your answers in...

Find the eigenvalues λn and eigenfunctions yn(x) for the given boundary-value problem. (Give your answers in terms of k, making sure that each value of k corresponds to two unique eigenvalues.)

y'' + λy = 0,  y(−π) = 0,  y(π) = 0

λ2k − 1 =, k=1,2,3,...

y2k − 1(x) =, k=1,2,3,...

λ2k =, k=1,2,3,...

y2k(x) =, k=1,2,3,...

Solutions

Expert Solution

Colby Messinger answered 2 years ago
Next > < Previous

Related Solutions

Find the eigenvalues λn and eigenfunctions yn(x) for the given boundary-value problem. (Give your answers in...
Find the eigenvalues λn and eigenfunctions yn(x) for the given boundary-value problem. (Give your answers in terms of n, making sure that each value of n corresponds to a unique eigenvalue.) y'' + λy = 0,  y(0) = 0,  y(π/6) = 0 λn =   , n = 1, 2, 3,    yn(x) =   , n = 1, 2, 3,   
Find the eigenvalues λn and eigenfunctions yn(x) for the given boundary-value problem. (Give your answers in...
Find the eigenvalues λn and eigenfunctions yn(x) for the given boundary-value problem. (Give your answers in terms of n, making sure that each value of n corresponds to a unique eigenvalue.) x2y'' + xy' + λy = 0,  y(1) = 0,  y'(e) = 0
Find the eigenvalues λn and eigenfunctions yn(x) for the given boundary-value problem. (Give your answers in...
Find the eigenvalues λn and eigenfunctions yn(x) for the given boundary-value problem. (Give your answers in terms of n, making sure that each value of n corresponds to a unique eigenvalue.) x2y'' + xy' + λy = 0,  y'(e−1) = 0,  y(1) = 0 λn = n = 1, 2, 3,    yn(x) = n = 1, 2, 3,   
Find the eigenvalues and eigenfunctions of the given boundary value problem. Assume that all eigenvalues are...
Find the eigenvalues and eigenfunctions of the given boundary value problem. Assume that all eigenvalues are real. (Let n represent an arbitrary positive number.) y''+λy= 0， y（0）= 0， y'（π）= 0
Find the eigenfunctions for the following boundary value problem. x2y?? ? 15xy? + (64 + ?)?y...
Find the eigenfunctions for the following boundary value problem. x2y?? ? 15xy? + (64 + ?)?y ?=? 0,    y(e?1) ?=? 0, ?y(1) ?=? 0. In the eigenfunction take the arbitrary constant (either c1 or c2) from the general solution to be 1
Find the linear space of eigenfunctions for the problem with periodic boundary conditions u′′(x) = λu(x)...
Find the linear space of eigenfunctions for the problem with periodic boundary conditions u′′(x) = λu(x) u(0) = u(2π) u′(0) = u′(2π) for (a) λ = −1 (b) λ = 0 (c) λ = 1. Note that you should look for nontrivial eigenfunctions
Find the eigenvalues and eigenfunctions for the following boundary value problem. y"+6y'-(L-8)=0, y(0)=0, y(2)=0 L ==...
Find the eigenvalues and eigenfunctions for the following boundary value problem. y"+6y'-(L-8)=0, y(0)=0, y(2)=0 L == Lambda
Find the eigenvalues and eigenfunctions of the problem y" + λy = 0 , y(−π/2) =...
Find the eigenvalues and eigenfunctions of the problem y" + λy = 0 , y(−π/2) = 0 , y(π/2) = 0. Please explain in detail all steps. Thank you
Determine the eigenvalues and the corresponding normalized eigenfunctions of the following Sturm–Liouville problem: y''(x) + λy(x)...
Determine the eigenvalues and the corresponding normalized eigenfunctions of the following Sturm–Liouville problem: y''(x) + λy(x) = 0, x ∈ [0;L], y(0) = 0, y(L) = 0,
Consider the given matrix. −1    2 −5    1 Find the eigenvalues. (Enter your answers...
Consider the given matrix. −1    2 −5    1 Find the eigenvalues. (Enter your answers as a comma-separated list.) λ = 3i,−3i (I got these right) Find the eigenvectors of the matrix. (Enter your answers in order of the corresponding eigenvalues, from smallest to largest by real part, then by imaginary part.) K1 = K2 = I can't seem to get the eigenvectors right.
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT