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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...
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...
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...
5. Consider the problem a2y"y _2.J 0 x1 = 0, y(0) 0, y(1= 0. (a) Put the problem in Sturm-Liouville form and explai...
5. Consider the problem a2y"y _2.J 0 x1 = 0, y(0) 0, y(1= 0. (a) Put the problem in Sturm-Liouville form and explain the nature of any singular points. (b) State the appropriate modified boundary conditions (c) Find all eigenvalues and eigenfunctions for the modified problem
5. Consider the problem a2y"y _2.J 0 x1 = 0, y(0) 0, y(1= 0. (a) Put the problem in Sturm-Liouville form and explain the nature of any singular points. (b) State the appropriate modified...
just put the eigenvalue and eigenfunctions would be good Consider the Sturm-Louiville problem d2y Ay 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...
Consider the Sturm-Louiville problem d2y +Ay 0, y(0) 0, '(5)= 0. dz2 With n defined as...
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.
2) For the Sturm-Liouville eigenvalue problem + λφ-0, dt2 do 0, dc (a) 0 verify the...
2) For the Sturm-Liouville eigenvalue problem + λφ-0, dt2 do 0, dc (a) 0 verify the following properties: a) The nth eigenfunction has (n-1) zeros on the open interval 0<x<a b) There are an infinite number of eigenvalues with a smallest, but no largest. c) What does the Rayleigh Quotient say about negative and zero eigenfunctions.
Determine the eigenvalues and eigenfunctions for the eigenvalue problem Hint: this is not a Stu...
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. 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
II. 1. Find the eigenvalues and the eigenfunctions for the following Sturm-Liouville problem X"+AX=0, x(0)=0, X'(TT)...
II. 1. Find the eigenvalues and the eigenfunctions for the following Sturm-Liouville problem X"+AX=0, x(0)=0, X'(TT) = 0
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...
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...
#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...
5. Consider the problem a2y"y _2.J 0 x1 = 0, y(0) 0, y(1= 0. (a) Put the problem in Sturm-Liouville form and explain the nature of any singular points. (b) State the appropriate modified boundary conditions (c) Find all eigenvalues and eigenfunctions for the modified problem
5. Consider the problem a2y"y _2.J 0 x1 = 0, y(0) 0, y(1= 0. (a) Put the problem in Sturm-Liouville form and explain the nature of any singular points. (b) State the appropriate modified...
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...
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.
2) For the Sturm-Liouville eigenvalue problem + λφ-0, dt2 do 0, dc (a) 0 verify the following properties: a) The nth eigenfunction has (n-1) zeros on the open interval 0<x<a b) There are an infinite number of eigenvalues with a smallest, but no largest. c) What does the Rayleigh Quotient say about negative and zero eigenfunctions.
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
II. 1. Find the eigenvalues and the eigenfunctions for the following Sturm-Liouville problem X"+AX=0, x(0)=0, X'(TT) = 0
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...
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