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dz de 02 -13 where dz dt 11 Z + [] 2 2 %3*م and Z [2]

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

Solve the system of differential equations given in matrix form for the general solution. We must do this by calculating the eigenvalues and eigenvectors. Note: we get a repeated eigenvalue and must solve for the second eigenvector to get two linearly independent solutions for our general solution.

dz
de
○ 2
-1 3
Z +
where dz
[]
○-34
=
and Z
높이] -2-12]
Zz

With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.

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Step 1: Objective:

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Step 2: Find th eigenvalues of A.

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Step 3: Find the eigenvectors.

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Step 4: Homogeneous solution:

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Step 5: Find the particular solution:

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Step 6: Find the general solution.

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