4. Draw the zeroclines (the functions of the vector space set equal to zero) for the following system of equations. dx dt dy dt = 2x2x² - xy,, = 2y - xy - 2y². (3) Use the zeroclines for a) to find the equilibrium points of the system. b) Label the equilibrium points in the drawing of the zeroclines and their coordinates. c) Calculate the Jacobian and classify each equilibrium point (source, spiral, sink, etc.).

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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SOLVE STEP BY STEP IN DIGITAL FORMAT
4. Draw the zeroclines (the functions of the vector space set equal to zero) for the following system
of equations.
d.x
dt
dy
dt
= 2x2x² - xy,,
= 2y - xy - 2y².
(3)
Use the zeroclines for a) to find the equilibrium points of the system. b) Label the
equilibrium points in the drawing of the zeroclines and their coordinates. c) Calculate the Jacobian and
classify each equilibrium point (source, spiral, sink, etc.).
Transcribed Image Text:SOLVE STEP BY STEP IN DIGITAL FORMAT 4. Draw the zeroclines (the functions of the vector space set equal to zero) for the following system of equations. d.x dt dy dt = 2x2x² - xy,, = 2y - xy - 2y². (3) Use the zeroclines for a) to find the equilibrium points of the system. b) Label the equilibrium points in the drawing of the zeroclines and their coordinates. c) Calculate the Jacobian and classify each equilibrium point (source, spiral, sink, etc.).
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