find the eigenvalues and the eigenfunctions for the equation y'' + (lambda)y = 0 where y(a) = 0, y(b) = 0 for a<b.
Find the eigenvalues and the eigenfunctions for the equation y'' + (lambda)y = 0 where y(a) = 0, ...
(1 point) Find the eigenvalues and corresponding eigenfunctions of 3 + y = 0, y(0) = 0, y(1) = 0 dx2 Eigenvalues: in = for n = 1,2,... The eigenfunction associated with the an is:
6. y"-2y4(λ + 1)y=0, y(0)=0, Eigenvalue problem: (a) Find the eigenvalues and eigenfunctions. (b) Determine the orthogonality relation between the eigenfuntions. y(l)-0, 0 x 1 6. y"-2y4(λ + 1)y=0, y(0)=0, Eigenvalue problem: (a) Find the eigenvalues and eigenfunctions. (b) Determine the orthogonality relation between the eigenfuntions. y(l)-0, 0 x 1
Find the eigenvalues and eigenfunctions for the differential operator L(y)=−y″L(y)=−y″ with boundary conditions y′(0)=0y′(0)=0 and y′(3)=0y′(3)=0, which is equivalent to the following BVP y″+λy=0,y′(0)=0,y′(3)=0.y″+λy=0,y′(0)=0,y′(3)=0. Find the eigenvalues and eigenfunctions for the differential operator L(y)--y" with boundary conditions y (0)0 and y' (3)-0, which is equivalent to the following BVP (a) Find all eigenvalues 2n as function of a positive integer n > 1. (b) Find the eigenfunctions yn corresponding to the eigenvaluesn found in part (a). Help Entering Answers ew...
please show work differential equation 1. Find the positive eigenvalues and the corresponding eigenfunctions of the boundary value problem -" +42y = 0; y(0) = 0, y(27) = 0. If the equation has no positive eigenvalues, then state so.
ind the eigenvalues and eigenfunctions of the regular Stu problem y(0) -2'(0() 0 ind the eigenvalues and eigenfunctions of the regular Stu problem y(0) -2'(0() 0
(1 point) In this problem we find the eigenfunctions and eigenvalues of the differential equation B+ iy=0 with boundary conditions (0) + (0) = 0 W2) = 0 For the general solution of the differential equation in the following cases use A and B for your constants, for example y = A cos(x) + B sin(x)For the variable i type the word lambda, otherwise treat it as you would any other variable. Case 1: 1 = 0 (1a.) Ignoring the...
Consider the following differential equation. Assume that all eigenvalues are real y" + λy 0, y(0) 0, y(n) + y'(n) 0 (a) Determine the form of the eigenfunctions n(x)-cos μηχ, where u2- O φ n(x)-1-μ tan(A), where-u2-λ 0 φ n(x)-sin μηχ, where μ2-λ O φ n(x)-1-μ cot(A), where-μ2-λ O φη(x) = 1-μ cot(A), where μ = λ Determine the determinantal equation satisfied by the nonzero eigenvalues O μη satisfies cot v/μ -V μ nn satisfies tan v/λπ-- νλ O An...
Find the eigenvalues and eigenfunctions for the boundary value problem, 2x 2 y 00 + 2xy 0 + λy = 0, y(1) = 0, y 0 (2) = 0.
please answer compleltly 2. Find the eigenfunctions and eigenvalues for the differential equation d^2u(x)/dr^2 = -k^2 u(x) in the interval 0 < = x < = a, assuming k is a real number, for the following sets of boundary conditions: (a) bu(0)+cdu/dt|x=0 =0 and bu(a)+cdu/dx|x=a =0 (b) u(0)+a du/dx|x=0 =0 and u(a)-adu/dx|x=a =0 You need not normalize the eigenfunctions. For (b), find the equation which determines the eigenvalues and verify that there is an infinite set of eigenfunctions and eigenvalues;...
Find the eigenvalues and eigenfunctions for the following boundary-value problem. xạy"+xy'+2y = 0, y'le')=0, y(1) =0)