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,

Solutions

Expert Solution

please comments if you have any problem

milcah answered 1 year ago

Next > < Previous

Related Solutions

Determine the eigenvalues and eigenfunctions of the following regular Sturm–Liouville systems: (a) y′′ + λy =...

Determine the eigenvalues and eigenfunctions of the following regular Sturm–Liouville systems: (a) y′′ + λy = 0, y′ (0) = 0 , y′ (π) = 0. (b) y′′ + λy = 0, y (1) = 0 , y(0) + y′ (0) = 0.

Find the eigenvalues and eigenfunctions of the Sturm-Liouville system y"+ lamda y = 0 o<x<1 y(0)...

Find the eigenvalues and eigenfunctions of the Sturm-Liouville system y"+ lamda y = 0 o<x<1 y(0) = 0 y'(1) = 0 (b) Show that the eigenfunctions Yn and Ym you obtained from the above are orthogonal if n not= m.

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

Find the eigenvalues of the problem: y'' + λy = 0, 0 < x < 2π,...

Find the eigenvalues of the problem: y'' + λy = 0, 0 < x < 2π, y(0) = y(2π), y' (0) = y'(2π) and one eigenfunction for each eigenvalue.

Consider Sturm-Liouville problem −u`` + q(x)u = λu , x ∈ (a, b), u(a) = 0,...

Consider Sturm-Liouville problem −u`` + q(x)u = λu , x ∈ (a, b), u(a) = 0, u(b) = 0. please can you find the eigenvalues and eigenfunction?

Consider the Sturm-Liouville problem X′′(x) + λX(x) = 0 subject toX′(0) = 0, X(l) = 0....

Consider the Sturm-Liouville problem X′′(x) + λX(x) = 0 subject toX′(0) = 0, X(l) = 0. Are the boundary conditions symmetric? Do these boundary conditions yield negative eigenvalues? Determine the eigenvalues and eigenfunctions, Xn(x). (It is enough in some cases to provide the equation that determines the eigenvalues rather than an explicit formula.) Are the eigenfunctions orthogonal?

Determine the eigenvalues and eigenfunctions of the following operator (assume σ(x) ≡ 1): L(u) = u''−2u...

Determine the eigenvalues and eigenfunctions of the following operator (assume σ(x) ≡ 1): L(u) = u''−2u x ∈ (−1,1) with periodic boundary conditions u(−1) = u(1), u'(−1) = u'(1). Box your ﬁnal answer

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

Show that the following are eigenfunctions of the Laplacian operator and determine the eigenvalues: a. (r^-1)sinkr...

Show that the following are eigenfunctions of the Laplacian operator and determine the eigenvalues: a. (r^-1)sinkr b.( r^-3)[(sin^2)θ]sin2φ

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,...

Subjects