What are the eigenvalues and eigenfunctions of the
Sturm-Louiville problem
ODE: X" + X = 0, 0 < x
< 1
BCs:
⇢
X(0) = 0
X(0) =
0
What are the functions p(x), q(x), and r(x) in the general
Sturm-Louiville
problem?
What are the eigenvalues and eigenfunctions of the Sturm-Louiville problem ODE: X" + X = 0, 0 <...
Determine the eigenvalues and eigenfunctions for the eigenvalue problem Hint: this is not a Sturm Liouville problem since the equation is not self-adjoint. Suggest a transformation of the dependent variable to reduce the problem to a self-adjoint one. We were unable to transcribe this image0 < x < π, y'(0) 1/ ( π) = 0 0
just put the eigenvalue and eigenfunctions would be good Consider the Sturm-Louiville problem d2y Ay 0, y0) 0, (5) 0. dr2 With n defined as taking values n = 1,2, 3, .., complete the following (a) Enter the eigenvalues. (b) Enter the eigenfunctions. yn = Consider the Sturm-Louiville problem d2y Ay 0, y0) 0, (5) 0. dr2 With n defined as taking values n = 1,2, 3, .., complete the following (a) Enter the eigenvalues. (b) Enter the eigenfunctions. yn...
II. 1. Find the eigenvalues and the eigenfunctions for the following Sturm-Liouville problem X"+AX=0, x(0)=0, X'(TT) = 0
Consider the Sturm-Louiville problem d2y +Ay 0, y(0) 0, '(5)= 0. dz2 With n defined as taking values n 1,2,3,..., complete the following. (a) Enter the eigenvalues. (b) Enter the eigenfunctions. Consider the Sturm-Louiville problem d2y +Ay 0, y(0) 0, '(5)= 0. dz2 With n defined as taking values n 1,2,3,..., complete the following. (a) Enter the eigenvalues. (b) Enter the eigenfunctions.
Partial Differential Equations: Calculate the eigenvalues and eigenfunctions for the eigenvalue problem associated with the vibrating string problem with homogeneous boundary conditions. i.e., , We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Please show working! If unsure of the answer please leave for someone else. Consider the Sturm-Louiville problem d2 y +2y 0 dr2 (0)0, y(3) 0. With n defined as taking values n 1, 2,3, ..., complete the following. (a) Enter the eigenvalues. An = (b) Enter the eigenfunctions Yn Consider the Sturm-Louiville problem d2 y +2y 0 dr2 (0)0, y(3) 0. With n defined as taking values n 1, 2,3, ..., complete the following. (a) Enter the eigenvalues. An =...
(20 points) For the following problem use separation of variables to identify the Sturm-Liouville Problem and its eigenvalues and eigenfunctions. DO NOT solve it. This is a steady state temper- ature problem in a cylinder where the temperature depends on ρ and z only. 4. Up(1,2) = 0, 0<z<1 a(p, 0) 0, u(p, 1) 5, 0 < ρ < 1 (20 points) For the following problem use separation of variables to identify the Sturm-Liouville Problem and its eigenvalues and eigenfunctions....
6. Determine the sequence of eigenvalues and corresponding eigenfunctions for each of the following Sturm-Liouville systems: (a) + Ap = 0, 9 (0) - 0) , 3º (2) + 5 °' (2) - 0) (b) 1 (0) + R -0, R'(1) - 0, R' (eº) - 0
#2 ONLY PLEASE 1. Consider the non-Sturm-Liouville differential equation Multiply this equation by H(x). Determine H(x) such that the equation may be reduced to the standard Sturm-Liouville form: do Given a(z), 3(2), and 7(2), what are p(x), σ(x), and q(x) 2. Consider the eigenvalue problem (a) Use the result from the previous problem to put this in Sturm-Liouville form (b) Using the Rayleigh quotient, show that λ > 0. (c) Solve this equation subject to the boundary conditions and determine...
6. Consider the eigenvalue problem 1 < x < 2, y(1) = 0, y(2) = 0. (a) Write the problem in Sturm-Liouville form, identifying p, q, and w. (b) Is the problem regular? Explain |(c) Is the operator S symmetric? Explain. (d) Find all eigenvalues and eigenfunctions. Discuss in light of Theorem 4.3 (e) Find the orthogonal expansion of f(x) = ln x, 1 < x < 2, in terms of these eigenfunctions. (f) Find the smallest N such that...