‘or the system below, find the general solution, sketch the trajectories, being careful to nclude the eigenvector directions, and classify the type of fixed point: x=y, y=-2(x + y). f the eigenvalues are complex, write the general system in terms of sines and cosines, as bove.
‘or the system below, find the general solution, sketch the trajectories, being careful to nclude the eigenvector directions, and classify the type of fixed point: x=y, y=-2(x + y). f the eigenvalues are complex, write the general system in terms of sines and cosines, as bove.
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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![For the system below, find the general solution, sketch the trajectories, being careful to include the eigenvector directions, and classify the type of fixed point:
\[
\dot{x} = y, \quad \dot{y} = -2(x + y).
\]
If the eigenvalues are complex, write the general system in terms of sines and cosines, as above.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F97e612ef-1556-436b-b62c-352b280e9e69%2F1b1668a7-a5db-402b-a28d-ce98466d5041%2Ff2eh094_processed.png&w=3840&q=75)
Transcribed Image Text:For the system below, find the general solution, sketch the trajectories, being careful to include the eigenvector directions, and classify the type of fixed point:
\[
\dot{x} = y, \quad \dot{y} = -2(x + y).
\]
If the eigenvalues are complex, write the general system in terms of sines and cosines, as above.
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