Find the eigenvalues and eigenfunctions of the boundary-value problemx2y′′+xy′+ 9λy= 0, y′(1) = 0,y(e) = 0.   Put the equation in self-adjoint form, and give an orthogonality relation   Show that if ym and yn are two eigenfunctions corresponding to two different eigenvalues λm and λn respectively, then ym and yn are linearly independent

Q: dx 8х — 9у dt dy = x + 2y x(0) = 2 y(0) = 1 - dt

A: The solution is given as

Q: Find the eigenvalues , and eigenfunctions y,(x) for the given boundary-value problem. (Give your…

A: Image is attached with detailed solution.

Q: 5. From the eigenvectors of S = AAT/(n-1), find the line and the plane closest to the following…

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Q: ut uxx + 3u = u(0,t) = u(n, t) = 0 (Do NOT show the details of finding the eigenvalues and the…

A: This is a problem of partial differential equation.

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Q: Apply the eigenvalue method to find a general solution of the given system. For the given initial…

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Q: Find the eigenvalues and eigenfunctions of the following regular Sturm-Liouville system y-py=0; y(0)…

A: The solution of this Strum Liouville problem is given by m2-μ=0⇒m2=μ⇒m=±μ Hence the general solution…

Q: = eat. Use 4. Consider the equation x" - 2ax' + a²x = 0, which has solution x = reduction of order…

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Q: Consider the linear system ● A₁ = = i a. Find the eigenvalues and eigenvectors for the coefficient…

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Q: (a) Find the eigenvalues and eigen-functions for the problem ƒ” (x) + \ƒ(x) = 0, f(0) = 0, ƒ'(2) = =…

A: (a)  f''(x)+λfx=0,   f0=0, f'2=0 Let λ=0 fx=ax+b⇒f0=0⇒b=0f'(2)=0⇒a=0 Therefore f(x)=0 For λ=-μ2…

Q: 3. Solue the ghen system by using the eigenvalue problem x': x - 5y y'- 2x-y.

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Q: Consider the Sturm-Liouville problem y" - 2y + (1 – 4A)y = 0, y(0) = 0, (1) – y(1) = 0. (a) Find the…

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Q: Find the eigenvalues A, and eigenfunctions y(x) for the given boundary-value problem. (Give your…

A: Given :- Calculating an Eigen value  and Eigen function for the given boundary value problem.To…

Q: Consider the Sturm-Liouville Problem?X²y" – 3xy'+  4λy = 0 , (1) = 0  y(3) = 0 Find all eigenvalues…

A: “Since you have asked multiple questions, we will solve the first question for you i.e. (a). If you…

Q: (b) For the following BVP, find all the eigenvalues and eigenfunctions: " - 2y + (A +1)y = 0, y(0) =…

A: Given: y''-2y'+λ+1y=0 characteristic equation will be D2-2D+λ+1y=0 on solving, D-12=-λ we will…

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Q: Solve Q

A: Given BVP, y''-2y'+λy=0;y0=0;  yπ=0 The auxiliary equation for the given differential equation can…

Q: dx = 2x + y dt K1 = K2 = dy -x dt ( = c1 + C2 et O A O B x = c ()e* + cz (",) e* X = C1 O D ||

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Q: 3 -4 dx 8. dt

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A: Let us consider system of differential equation: X'=AX Find the eigenvalues of matrix A. let us say…

Q: dx dt dy dt || -1.6x + 0.5y, 2.5x - 3.6y.

A: Given  the system of differential equation,            let      ,then system can be written as…

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: 2. For the following systems with complex eigenvalues, find the general solutions: -5 ›× - ( 13³ ) ×…

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Q: Find the eigenvalues , and eigenfunctions y,(x) for the given boundary-value problem. (Give your…

A: For a given boundary value problem find the cases for which the equation has non trivial solutions.…

Q: One solution of t + 2 t =x² + t + 2 is x₁ (t) = t. Find a second independent X1 - x = 0 t² solution.

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Q: Find the eigenvalues 1, and eigenfunctions y,(x) for the given boundary-value problem. (Give your…

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Q: Find all positive eigenvalues and eigen functions for the Sturm-Liouville y" + xy = 0, y'(0) = 0, t…

A: .....

Q: Q1) Consider the problem y " +2y= 0, y' (0) = 0, y(1) = 0. a) Find the eigenvalues and the…

A: We have to find the eigen value and eigen function.