Answered: 9.9. Solve the system of differential…

9.9. Solve the system of differential equations dx dt dy dt with the initial conditions x(0) = 1, y(0) = -1. = 5x – 2y = 7x - 4y, 9 4 2t 3t 9.9 x = = ²e³t - ²e-²t, y = ²e³t - 14e-2t. 5 5

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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Question

I'm encountering challenges in solving this problem solely using matrix notation, and I'm seeking your guidance. The problem specifically calls for a solution exclusively in matrix notation, without any other methods. Could you please provide me with a detailed, step-by-step explanation in matrix notation to help me solve the problem and reach the final solution?

9.9. Solve the system of differential equations
dx
dt
dy
dt
with the initial conditions x(0) = 1, y(0) = -1.
= 5x – 2y
= 7x - 4y,

9
4 2t
3t
9.9 x =
= ²e³t - ²e-²t, y = ²e³t - 14e-2t.
5
5

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Step 1: Determine the given values

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Step 2: Matrix form of the differential equation

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Step 3: Find the eigenvalues of the matrix

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Step 4: Find the eigenvectors of the matrix

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Step 5: To find the general solution

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Step 6: To find the particular solution

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