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x' = y y' = -6x – 5y (1) Find all straight line trajectories for the system above, using any method from class. (That is, find the equa- tions of any lines that appear in the phase plane.) Then, find the fundamental solutions corresponding to these lines and state the general solution to the system. (2) Find the solution with initial condition (6,6). Reach: Make a rough sketch of the phase plane that indicates the features you found above, as well as the solution curve passing through (6,6). Add a few arrows to indicate how solutions behave over time.

x' = y y' = -6x – 5y (1) Find all straight line trajectories for the system above, using any method from class. (That is, find the equa- tions of any lines that appear in the phase plane.) Then, find the fundamental solutions corresponding to these lines and state the general solution to the system. (2) Find the solution with initial condition (6,6). Reach: Make a rough sketch of the phase plane that indicates the features you found above, as well as the solution curve passing through (6,6). Add a few arrows to indicate how solutions behave over time.

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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Answer all parts of the DE problem

x' = y y' = -6x – 5y (1) Find all straight line trajectories for the system above, using any method from class. (That is, find the equa- tions of any lines that appear in the phase plane.) Then, find the fundamental solutions corresponding to these lines and state the general solution to the system. (2) Find the solution with initial condition (6,6). Reach: Make a rough sketch of the phase plane that indicates the features you found above, as well as the solution curve passing through (6,6). Add a few arrows to indicate how solutions behave over time.
Transcribed Image Text:x' = y y' = -6x – 5y (1) Find all straight line trajectories for the system above, using any method from class. (That is, find the equa- tions of any lines that appear in the phase plane.) Then, find the fundamental solutions corresponding to these lines and state the general solution to the system. (2) Find the solution with initial condition (6,6). Reach: Make a rough sketch of the phase plane that indicates the features you found above, as well as the solution curve passing through (6,6). Add a few arrows to indicate how solutions behave over time.
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