4x + y dy x + 2y dt a) Find the general solution for x(t) and y(t) b) Solve the initial value problem x(0) = 1, y(0) = 1 • Your answer should include the eigenvalues and corresponding eigenvectors • All your work dt =

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A: The eigen values λn and the eigen functions yn of the Strum-Liouville problem: y''+9λy=0,…

Q: 2. Consider the following IVP y" + 5y +6y=0, y(0) = 2, y'(0) = 3. (a) Write the ODE as a system of…

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Q: Consider the following Sturm-Liouville problem: (e"d')' + de®¢ = 0, 0<x < a, $(0) = 0, (a) = 0. (1)…

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Q: Find a particular solution of (;) ;)-(: :) (;) - (*) -5 sint 4 -4t A

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Q: Q6) (Eigenvalue problem) Consider the eigenvalue problem y" + 2y + Ay = 0, y(0) = 0, y(1) = 0, where…

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Q: 2. x' = Find the general solution of the system of equations. -20 28 8 -14 22 4 X -21 21 14

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Q: 5. Consider the ordinary differential equation Orx + Ao = 0 (a) Determine the eigenvalues An and…

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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…

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

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Q: Using Elgenvalues and Eigenvectors   Dx/ dt= y Dy/dt=2x

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

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Q: d the eigenvalues and eigenfunctions for the following boundary value proble y" + Xy = 0 with y'(0)…

A: Given the equation y''+λy=0 with y'0=0, y'2=0. Consider the auxiliary equation,  r2+λ=0r=±λi…

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Q: 2 2 -6 8. The general solution of x' = x is: (Hint: 6 is an eigenvalue.) 2 -1 -3 -2 - 1 -2 3 1 (a) x…

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Q: Find the eigenvalues and eigenfunctions for the following eigenvalue problem: X"+AX=0, A>0. X(0)=0,…

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Q: |=0. 元一。

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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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