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.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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answer first part please

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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