Question

Sturm-Liouville problem:

y′′+λy= 0, y′(0) = 0, y(1) +y′(1) = 0.

Determine the four smallest eigenvalues and corresponding eigenfuntions.

For lambda = 0, < 0, > 0

Answer #1

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Sturm-Liouville problem: y′′+λy= 0, y′(0) = 0, y(1) +y′(1) = 0.
Determine the four smallest eigenvalues and corresponding
eigenfuntions. Please do it for lambda = 0, < 0, > 0. I'm
strugeling with the basics. Help would be appreciated.

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

a)Find the eigenvalues and eigenfunctions of the Sturm-Liouville
system
y"+ lamda y = 0
y(0) = 0
y'(1) = 1
I got y=x and y=sin((sqrt k)x)/((sqrt k) cos(sqrt k))
Please do b
(b) Show that the eigenfunctions Yn and Ym you obtained from the
above
are orthogonal if n not= m.

in
the Theory of sturm-Liouville it is said that any linear operator
of second order L(y)=b_0(x)y''+b_1(x)y'+b_2(x)y can be write as an
autoadjunt operator of Sturm-Liouville. Determine the integrant
factor and write the operator in the form of Sturm-Liouville
operator.

find the eigenvalues and eigenfunctions for the given
boundary-value problem.
y'' + (lambda)y = 0, y(-pi)=0, y(pi)=0
Please explain where alpha = (2n+1)/2 comes from in the
lambda>0 case. Thank you!!

Find all eigenvalues and corresponding eigenfunctions for the
following boundary value problem (x^2)y'' + λy = 0, (1 < x <
2), y(1) = 0 = y(2) and in particular the three cases μ < 1/2, μ
= 1/2, and μ > 1/2 associated with the sign and vanishing of the
discriminant of the characteristic equation

Consider the boundary value problem below (assume λ > 0): y
′′ + λy = 0 y(0) = 0 y ′ (π) = 0 Find the eigenvalues and the
associated eigenfunctions for this problem. Show all work.

find the eigenvalues and the eigenfunctions for the equation y''
+ (lambda)y = 0 where y(a) = 0, y(b) = 0 for a<b.

Convert the problem into a first order system of equations.
Determine the eigenvalues of the resulting matrix, and use the
eigen values to determine whether or not the solution decays to a
constant value.
y''+3y'+5y=0
y(0)=0
y'(0)=1

Given: The following boundary value problem:
y"+ lamda*y = 0;
0 < x < 2; y(0) =
0; y’(2) = 0
Find corresponding eigenvalues, (lamda)n
and normalized eigenfunctions yn
Expand the function f(x) = x, in terms of the eigen functions
obtained in (i)

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