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: Q1. a. Find the eigen values of the following matrix and discuss the applications of eigen values in…

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

A: Image is attached with detailed solution.

Q: x1(t) Let x(t) = be the solution to the discrete dynamical system: x2(t) x1(t + 1) = −8x1(t) +…

A: To solve this discrete dynamical system, we first find the eigenvalues and eigenvectors of the…

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.

Q: Consider the linear system a. Find the eigenvalues and eigenvectors for the coefficient matrix.…

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Q: a) Let A be the 2x2 matrix with eigenvalues 2 = 4,-1 such that E span E = span %3D Find both the…

A: Given:(a) A is  a 2×2 matrix with eigen value's λ=4,-1 and E4=span31 ,E-1=span12.  To find: Ak and…

Q: Show that the eigenvalues of the Sturm-Liouville system dy + Ay = 0 dx? y(0) = 0, y(L) = 0 %3D gre…

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Q: Apply the eigenvalue method to find the general solution and the corresponding particular solution:…

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

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Q: Show that the eigenvalue problem 2²y"+ 2ry+ (32² + (2² +1³) v = 0₁ y = 0, y(-1)= y(1) = 0, with…

A: We need to show that the functional and the constraint  can form the eigenvalue problem

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

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Q: Islder Hermites equdtion y" – 2æy + 4y = 0 and verify for yourself that y1 = 1 – 2x2 is a solution.…

A: Given differential equation is y''−2xy'+4y=0

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

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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: Use the method of separation of variables to construct the energy eigenfunctions for the particle…

A: Given equation: -h22m∂2Φn(x,y)∂x2+∂2Φn(x,y)∂y2=EnΦn(x,y), ∂2Φn(x,y)∂x2+∂2Φn(x,y)∂y2=-2mh2EnΦn(x,y),…

Q: the eigenvalues and hn and eigenfunctions un(x) for the boundary value problem. u" + h2u = 0,…

A: It is given that, the boundary value problem (B.V.P.) is u"+h2u=0, u(1)=u'(0)=0. We have to derive…

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: Consider the linear system 3 *' = Find the eigenvalues and eigenvectors for the coefficient matrix.…

A: The complete solutions are given below

Q: 3. Find the eigenvalues and the corresponding eigenfunctions of the Sturm-Liouville system y" +ày =…

A: Sturm liovuvilles system of differential equation

Q: Find the matrix A of the quadratic form assoe 2x2 - 3xy - 2y2 + 11 = 0 A = Find the eigenvalues of…

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Q: For the system of differential equations, = A₁, A₂ = U₁ = U2 = y' a) Find the characteristic…

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Q: Find the eigenvalues i, and eigenfunctions y,(x) for the given boundary-value problem y" + Ay = 0,…

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Q: The matrix T has eigenvalues and eigenvectors: • v = 1 with A =1. -1 1 with = 0. • V3 with A- Sive…

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Q: u = 2 uzz) 0 0 with boundary/initial conditions: u(0, t) = 0, u(6, t) = 0, S 2, 0<z<3 1 0, 3 < a < 6…

A: Given that,  ut=2uxx,  0&lt;x&lt;6,  t≥0⋯⋯(1) BC: Ux(0,t)=0, ux6,t=0 IC: ux,0=2,  0&lt;x≤30,…

Q: If my matrix contributes eigenvalue A = 3+ 4i with corresponding eigenvector v = [i, 1]. What are…

A: We will find out the required solution.

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: Let vn = be the solution to the discrete dynamical system: Yn 6xn – 13yn Yn+1 = 0xn – 7yn Xn+1 -3 If…

A: Using diagonalisation of the coefficients matrix.