П Write the function f(x) = x (1-x) as an eigenfunction ex- pansion of the eigenfunctions corresponding to the Sturm-Liouville prob- lem y" + Xy = 0, 0 < x < y(0) = 0 y (H) = 0 πT

Q: Find all eigenvalues and eigenfunctions of the following eigenvalue problem: X"+AX = 0. X (0) =…

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Q: Using the attached theorms, Solve dx/dt =2x+4y , dy/dt=-x+6y

A: Reference: Differential Equations, Linear Algebra

Q: Suppose that all the eigenvalues of the matrix A have negative real part. Then every solution of the…

A: Consider the provided question, Suppose that all the eigenvalues of the matrix A have negative real…

Q: f(x)=-x1²-6x2²-4x1+8x2+143 3- Find the critical points (optimum points) of the function f (x) = -…

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Q: Let vk = Yk () Consider the difference equation vk+1 = Avk with initial condition vo = where A is a…

A: Consider the given difference equation.

Q: Consider the eigenvalue problem y" + 2y' + ày = 0; y(0) = y(1) = 0. Show that there is no eigenvalue…

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Q: Find all the Eigen-values and Eigen-functions for the following BVP. y" + ly = 0 with y(-n) = y(n) ,…

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Q: 30. E=2*10^5 I=30000 L=600 W=25 y = dy dx = W 120EIL 3 (-x ² + 21³x² - (^x) W 120EIL (-5X² +…

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Q: . Prove that the matrix A = Cos 0 sin 0 - sin 0 cos - has no real eigenvalues for 0 < 0 < T.

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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: the eigenvalues/ eigenfunctions of y'' = λy y'(0) = 0 y(3) = 0

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Q: y" + Ay = 0, y(-2) = y(2), 3/(-2) = y'(2) %3D

A: Given         y''+ λy = 0,        y -2=y2,     y'(-2)=y'2 ........(1)

Q: a that have the same boundary curve and orientation. ., True, False or Indeterminate: If S is a…

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Q: Suppose the size of a population evolves according to the logistic equa- tion: dN = 1.5N dt N 100…

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Q: The eigenvalues for y" + Ay = 0, y(0) = 0; y'(#) = 0 are

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Q: (8) Find all eigenvalues and eigenvectors of the derivative map, D, on P₁ (R).

A: The set of polynomials of at most degree n over the real numbers Pn(R)…

Q: The eigenfunctions for y"-2y + Ay = 0, y(0) = 1, y(1) = 0 are O {e I sin ()}, n-1 O {e² sin(")},…

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Q: Suppose A E L(R") has a real eigenvalue \ < 0. Then the equation x' = = Ax

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Q: if \phi 1(x) and \phi 2(x) are two normalized eigen functions and \phi (x) = c1\phi 1(x) + c2\phi…

A: If ϕ1(x) and ϕ2(x) are two normalized eigen functions and ϕ(x)=c1ϕ1(x)+c2ϕ2(x) is also a normalized…

Q: Find all solution to the eigenvalue problem -X" =XX. X(-L) = X (L) & X'(−L) = X ' (L)

A: The given problem is to find the all solutions for the given eigen value problem with given boundary…

Q: E=2*10^5 I=30000 L=600 W=25 y = dy dx W 120EIL = 120 FIL (-5X² + 6(³X²-1²) ū assume as р 38, P = =…

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Q: use eigen Vealue and to s0lve eigen vee velbor 4

A: Here the given differential equation is of the form X'=AX First we calculate the eigenvalues and…

Q: 27. (Critical point) What kind of critical point does y' = Ay have if A has the eigenvalues -6 and…

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Q: Help me to solve it please

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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: None

A: To find the eigenvalues and eigenfunctions for the differential equation:y'' - 2y' + (1 + lambda)y =…

Q: Solve the IVP 22 + 1ox+1 %3D y Co) =0, y'(0) = -6 Osi ng the quasi-polynomial method.

A: y''-3y'-4y=0 D2-3D-4=0 D2 -4D+D-4=0 (D+1)(D-4)=0 D=-1,4 Complementary function =c1e-x +c2e4x

Q: The eigenvalues are λ₁ < λ2 < A3 < №4, where A₁ = has an eigenvector eigenvector A = -37 15 0 0 -70…

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Q: Question 3. Consider the eigenvalue problem U"(x) + XU (x) = 0, 0<x< l with the mixed boundary…

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Q: x=12²2 ²1x X find the eigenvalues and eigenvectors -Classify the critical point (0.0) as to type

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Q: What is the eigenvalue for the eigenfunction e^4ix of the operator ((d^2)/(dx^2))+(d/dx)−4i?

A: The solution is given as

Q: USING ELGEN VALUE x' SOLve EIGEN VECIOR 2'

A: