Solve the following initial value problems for the systems of equations using the matrix method. Findeigenvalues and eigenvectors by hand (but you can use technology to check your answers)(a)(b)x' =y'Ix2-6x + 3y-4x-y22x1 - 5x24x1 - 2x2x(0) = 3, y(0) = -2.2₁ (0) = 1, ₂ (0) = 1.7

Given system: a) x'=6x+3y; y'=-4x-y Initial conditions: x0=3, y0=-2. b) x1'=2x1-5x2; x2'=4x1-2x2…

Answered: Solve the following initial value…

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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The eigenvalues of the coefficient matrix can be found by inspection or factoring. Apply the eigenvalue method to find a general solution of the system. x₁ = 8x₁ + 3x₂ + 8x3, x'₂ = 3x₁ + 13x₂ + 3x3, x'3 = 8x₁ + 3x₂ + 8x3 What is the general solution in matrix form? x(t)

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Solve the following initial value problems for the systems of equations using the matrix method. Find eigenvalues and eigenvectors by hand (but you can use technology to check your answers) (a) (b) y' = x₁ = x2 6x + 3y -4x- -y 7 2x1 - 5x2 4x1 - 2x2 x(0) = 3, y(0) = -2. , *₁(0) = 1, ₂(0) = 1.