2) in the following Sturm-Liouville Boundary Value Problem y" + y =0, y(0) = 0 and y(1) = 0 The Eigen-function is given in the formula 0,(x) = c, sin(nnx) then: 1) Determine the normalized Eigen-function. 2) Expand the function f(x) 6, Osxs1 in the terms of normalized Eigen- function.

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A: First condition should be y(0)=0, from the given answer there is no option such that y(0)=1.

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A: Consider the given difference equation.

Q: 2. Show that eigenvalues A of the boundary value problem y" + (Ar +a)y = 0, y(0) – /(1) = 0, y/(0) +…

A: Given:   y"+(λx+x2)y=0, y(0)-y'(1)=0, y(0)+y'(1)=0

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Q: Find the Eigenvalues and Eigen Functions for the given boundary value problem y" + Ay= 0, y(0)= 0,…

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Q: 1. Find the eigenvalues and eigenfunctions of the boundary value problem y" +y' + Ay = 0, y(0) = 0,…

A:

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A: See the detailed solution below.

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A: Solution

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A: Given, the system of equation                           We have to find the solution of this system.

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A: "Since you have posted a question with multiple subparts, we will solve first three subparts for…

Q: 2. Use Eigenvalue method to find the general solution of the given system dx 5 + 2y dx 3x + 2y + 42…

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Q: 6. Solve the boundary value problem y" – 2y' + Ay = 0 (0 < x < n) with y(0) = 0; y(n) = 0. Also…

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Q: What are the Eigenvalues of the system below: * dx 2x + y dt dy = -X dt О 01 O 1,1 О 1 О 11

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Q: Find the Eigenvalues and Eigen Functions for the given boundary value problem +ày =0, y(0)=0, y = 0.…

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Q: find the eigenvalues and cortespanding eigen functions for the_followng boundary valve problem on…

A: Hi! As per norms, we will be answering only the first question. If you need an answer to others then…

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A: Using diagonalisation of the coefficients matrix.

Q: 8. Consider the following system of differential equation: = x + y – 2 dt dy = - y + 3x +1 dt (a) )…

A: According to the given information, Consider the given system of differential equation.

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Q: [15] Solve the eigenvalue problem X"(x) + X'(x) - XX(x) = 0 X (0) = 0, X(a) = 0. 0<x<a,

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Q: 12- The system x' = x + 4y, y' = y + x has two eigenvectors.

A:

Q: What are the eigenvalues and eigenfunctions: x′′ + λx = 0, x(1) = x(3), x′(1) = x′(3) - Definey by…

A: The original differential equation is x''(z) +λ·x(z) =0 with given conditions x(1)=x(3) and…

Q: 1. Find the eigenvalues of A and the corresponding eigenvectors. 2. Use the results in 1. above to…

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Q: Problem 3: Is the maximum eigenvalue of Ag at most the maximum degree of G?

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A: Given that, xn+1=6xn-13yn             (1)yn+1=0xn-7yn               (2) and  v0→=-3-1, i.e⇒x0=-3,…

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A: Solution