5. Apply the eigenvalue method to find the general solution of the given system. Fina diso ahecorresponding particular solution by using the initial values.(x = 9x1 + 5x2x½ = -6x1 – 2x2Initial: x, (0) = 1,x2(0) = 0

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Answered: 5. Apply the eigenvalue method to find…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Consider the linear system X' = [223] -2 X. 1. Show that the eigenvalues of the given system are complex. 2. Find the general solution of the system.
For a linear DDS with multiple equations, assume that A is the matrix of the system with eigenvalue c and eigenvector u. Which of the following is true? Check all that apply. X(n) = A"X(0) is the recursive equation for the DDS □X(n) = A"X(0) is the explicit solution for the DDS □X(n) = AX(n − 1) is the recursive equation for the DDS We can always compute X(n) as X(n) = c"X(0) using the eigenvalue c We can compute X(n) as X(n) = X(0) when X(0) is a multiple of
Consider the Initial Value Problem: x₁ x2 X₁ = 0,₁ % v1 = 2x1 + 2x2 = = -4x12x₂² x1 (0) = 4 x2 (0) 6 (a) Find the eigenvalues and eigenvectors for the coefficient matrix. 181 = , and X₂ = ₁0₂ = (b) Solve the initial value problem. Give your solution in real form. x1 x2 = An ellipse with clockwise orientation phase plotter pplane9.m in MATLAB to describe the trajectory. [B] 1. Use the
mm.2
b) A system of differential equation is given as follows: x₁ = 9x₁ - 4x₂ x₂ = 8x₁ - 3x₂ where x₁ and X2 are functions of . Given that the eigenvalues of A= and 5 with the corresponding eigenvectors i) Write a matrix P that diagonalizes A. ii) Write a diagonal matrix D such that P¹ AP = D. iii) Hence, find the general solution to the system. [4=[83] are 1 and respectively.
Consider the linear system dx₁ dt dx₂ dt = 4x1 - 3x₂ = 3x1 + 4x2. 1. Show that upon conversion to the form X'= AX, the eigenvalues of A are complex. 2. Find the general solution of the system.
1. For the system below, find the general solution, sketch the trajectories, being careful to include the eigenvector directions, and classify the type of fixed point: x = x, ÿ y = 2x - 5y.
Apply the eigenvalue method to solve the initial value problem
Consider the initial value problem 4x2, x1(0) = 2, -4x1 + 8x2, x2(0) = 6. Find the eigenvalue A, an eigenvector v1, and a generalized eigenvector v2 for the coefficient matrix of this linear system. 1 4,4 1 1 help (numbers) help (matrices) Find the most general real-valued solution to the linear system of differential equations. Use c and c2 to denote arbitrary constants, and enter them as "c1" and "c2". x1(t) cle^(4t) help (formulas) x2 (t) help (formulas) Solve the original initial value problem. x1(t) : 4e^(4t) help (formulas) x2(t) : 4e^(4t)+2 help (formulas)
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5. Apply the eigenvalue method to find the general solution of the given system. Find aiso the corresponding particular solution by using the initial values. Sxi = 9x, + 5x2 lx2 = -6x1 - 2x2 Initial: x, (0) = 1,x2(0) = 0 %3D