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Suppose that A has two eigenvalues, A1 = 0 with eigenvector v and A, # 0 with eigenvector v2. 1. Write down the general solution of the equation i = Ax. 2. After changing to a coordinate system referred to the eigenvectors the equation will become dã a. dt By solving the equation, draw the phase portrait in the (i, g) system, and hence sketch the phase portrait for the original coordinates. 3. Draw the phase portrait for the equation de -2 x. dt

Suppose that A has two eigenvalues, A1 = 0 with eigenvector v and A, # 0 with eigenvector v2. 1. Write down the general solution of the equation i = Ax. 2. After changing to a coordinate system referred to the eigenvectors the equation will become dã a. dt By solving the equation, draw the phase portrait in the (i, g) system, and hence sketch the phase portrait for the original coordinates. 3. Draw the phase portrait for the equation de -2 x. dt

Advanced Engineering Mathematics
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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Suppose that A has two eigenvalues, A = 0 with eigenvector v, and A2 # 0 with eigenvector V2. 1. Write down the general solution of the equation à = Ax. 2. After changing to a coordinate system referred to the eigenvectors the equation will become dt By solving the equation, draw the phase portrait in the (ã, j) system, and hence sketch the phase portrait for the original coordinates. 3. Draw the phase portrait for the equation dæ -2 x. dt 1
Transcribed Image Text:Suppose that A has two eigenvalues, A = 0 with eigenvector v, and A2 # 0 with eigenvector V2. 1. Write down the general solution of the equation à = Ax. 2. After changing to a coordinate system referred to the eigenvectors the equation will become dt By solving the equation, draw the phase portrait in the (ã, j) system, and hence sketch the phase portrait for the original coordinates. 3. Draw the phase portrait for the equation dæ -2 x. dt 1
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