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.
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 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?
1a.) find the eigenvalues of x"+(lambda)(x) = 0, x(0)=x'(pi)=0
1b.) Solve ut=((c)^2)u(xx) , u(0,x)= alpha * sin x, with the boundary condition u(t,0)=u(t,pi)=0
1c.) Solve ut = u(xx), u(0,x) = alpha * sin ((pi*x)/(L)), with the boundary condition u(t,0) = u(t,L) = 0.
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