Problem 5. Consider the following 2 × 2 linear system of differential equations. (x₁'(t) = 5x1(t) — 6x2(t) |x2'(t) = 2x1(t) — 2x2(t) when x₁(0) : |x2(0) = 1 = 3 (a) Write this IVP (including the initial conditions) in matrix-vector form, with x(t) = (x(t)) (b) Find eigenvalues and eigenvectors of corresponding coefficient matrix. Label them clearly. (c) Construct the general solution of the system given above in Eq. (15) (d) Find the particular solution. For your final answer, write down explicitly the pair of real-valued solutions, x₁ (t) and x2(t), in the box below. X, (+)= X₂ (+)=
Problem 5. Consider the following 2 × 2 linear system of differential equations. (x₁'(t) = 5x1(t) — 6x2(t) |x2'(t) = 2x1(t) — 2x2(t) when x₁(0) : |x2(0) = 1 = 3 (a) Write this IVP (including the initial conditions) in matrix-vector form, with x(t) = (x(t)) (b) Find eigenvalues and eigenvectors of corresponding coefficient matrix. Label them clearly. (c) Construct the general solution of the system given above in Eq. (15) (d) Find the particular solution. For your final answer, write down explicitly the pair of real-valued solutions, x₁ (t) and x2(t), in the box below. X, (+)= X₂ (+)=
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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