6. y"-2y4(λ + 1)y=0, y(0)=0, Eigenvalue problem: (a) Find the eigenvalues and eigenfunctions. (b)...
please solve all 3 Differential Equation problems 3.8.7 Question Help Consider the following eigenvalue problem for which all of its eigenvalues are nonnegative y',thy-0; y(0)-0, y(1) + y'(1)-0 (a) Show that λ =0 is not an eigenvalue (b) Show that the eigenfunctions are the functions {sin α11,o, where αη įs the nth positive root of the equation tan z -z (c) Draw a sketch indicating the roots as the points of intersection of the curves y tan z and y...
1. (5 points) Solve the following eigenvalue problem, i.e. find all eigenvalues and eigenfunctions of the problem y" + (1 - 5)y=0, 0<<<1, 7(0) = y(1) = 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
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...
Solve part (d) 6. Consider the eigenvalue problem 2"xy3y Ay 0 y(1)0, y(2)= 0. + 1 < x< 2, (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 ln x, 1 < 2, in terms of these (e) Find the orthogonal expansion of f(x) eigenfunctions _ 6. Consider the eigenvalue problem 2"xy3y...
7. Consider the eigenvalue problem y(0) = 0, y( 1 ) = 0. points b) State the appropriate modified boundary conditions c) Find all eigenvalues and eigenfunctions for the modified problem.
ZILLDIFFEQMODAP11 5.2.013. Find the eigenvalues λn and eigenfunctions yn(x) for the given boundary-value problem. (Give your answers in terms of n, making sure that each value of n corresponds to a unique eigenvalue.) y" + λy = 0, y'(0)= 0, y'(π) = 0
: Solve the following differential equation eigenvalue problems. a y'' + λy = 0; y(0) = 0; y(4) = 0 b y''+ λy = 0; y(0) = 0; y' (1) − 2y(1) = 0 In problem [a] you may assume that there are no eigenvalues for λ ≤ 0. In problem [b] you will not be able to find the exact eigenvalues. You should find a condition on the eigenvalues of the form f(µ) = 0 where µ 2 =...
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
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...