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Problem 1. Show that the eigenvalue problem -X"(r) - XX(X), X(-) = X(L),X'(-) = X(L) has...
12. Consider the unusual eigenvalue problem ux(0) = ur(l) = v(1)-U(0) (a) Show that 2 0 is a double eigenvalue. (b) Get an equation for the positive eigenvalues a>0. 102 CHAPTER 4 BOUNDARY PROBLEM...
12. Consider the unusual eigenvalue problem ux(0) = ur(l) = v(1)-U(0) (a) Show that 2 0 is a double eigenvalue. (b) Get an equation for the positive eigenvalues a>0. 102 CHAPTER 4 BOUNDARY PROBLEMS (c) Letting γ-IVA, reduce the equation in part (b) to the equation γ sin γ cos γ = sin (d) Use part (c) to find half of the eigenvalues explicitly and half of (e) Assuming that all the eigenvalues are nonnegative, make a list of (t)...
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)...
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...
verify the eigenfunctions of the problem 12. (a) Verify that the eigenfunctions of the problem n...
verify the eigenfunctions of the problem
12. (a) Verify that the eigenfunctions of the problem n are y"(x) = cos (x + π), n=0,1,2, (b) Show that the eigenfunctions in part (a) are orthogonal on , . (Hint: Use the trigonometric identity sin A cos B =-sin (A + B) +、sin (A-B).) Obtain the orthonormal set of eigenfunctions for the problem in part (a). (e)
6. Consider the eigenvalue problem 1 < x < 2, y(1) = 0, y(2) = 0. (a) Write the problem in Sturm-Liouville form,...
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...
6. y"-2y4(λ + 1)y=0, y(0)=0, Eigenvalue problem: (a) Find the eigenvalues and eigenfunctions. (b)...
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
Solve part (d) 6. Consider the eigenvalue problem 2"xy3y Ay 0 y(1)0, y(2)= 0. + 1 < x< 2, (a) Write the proble...
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...
1. (5 points) Solve the following eigenvalue problem, i.e. find all eigenvalues and eigenfunctions of the...
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.
7. Consider the eigenvalue problem y(0) = 0, y( 1 ) = 0. points b) State...
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.
1. Consider the non-Sturm-Liouville differential equation Multiply this equation by H(x). Determi...
#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...
(4 points) This problem is concerned with solving an initial boundary value problem for the heat ...
(4 points) This problem is concerned with solving an initial boundary value problem for the heat equation: u,(x, t)- uxx(x,), 0
12. Consider the unusual eigenvalue problem ux(0) = ur(l) = v(1)-U(0) (a) Show that 2 0 is a double eigenvalue. (b) Get an equation for the positive eigenvalues a>0. 102 CHAPTER 4 BOUNDARY PROBLEMS (c) Letting γ-IVA, reduce the equation in part (b) to the equation γ sin γ cos γ = sin (d) Use part (c) to find half of the eigenvalues explicitly and half of (e) Assuming that all the eigenvalues are nonnegative, make a list of (t)...
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...
verify the eigenfunctions of the problem
12. (a) Verify that the eigenfunctions of the problem n are y"(x) = cos (x + π), n=0,1,2, (b) Show that the eigenfunctions in part (a) are orthogonal on , . (Hint: Use the trigonometric identity sin A cos B =-sin (A + B) +、sin (A-B).) Obtain the orthonormal set of eigenfunctions for the problem in part (a). (e)
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...
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
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...
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.
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.
#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...
(4 points) This problem is concerned with solving an initial boundary value problem for the heat equation: u,(x, t)- uxx(x,), 0
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