Draw the phase diagram of the system; list all the equilibrium points; determine the stability of the equilibrium points; and describe the outcome of the system from various initial points. You should consider all four quadrants of the xy-plane. Include the coordinate axes; all the isoclines; all the equilibrium points; the allowed directions of motion (both vertical and horizontal) in all the regions into which the isoclines divide the xx, plane; direction of motion along isoclines, where applicable. dx dt =7-y, dy dt =x-7.
Draw the phase diagram of the system; list all the equilibrium points; determine the stability of the equilibrium points; and describe the outcome of the system from various initial points. You should consider all four quadrants of the xy-plane. Include the coordinate axes; all the isoclines; all the equilibrium points; the allowed directions of motion (both vertical and horizontal) in all the regions into which the isoclines divide the xx, plane; direction of motion along isoclines, where applicable. dx dt =7-y, dy dt =x-7.
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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Transcribed Image Text:Draw the phase diagram of the system; list all the equilibrium points; determine the stability of the
equilibrium points; and describe the outcome of the system from various initial points. You should
consider all four quadrants of the xy-plane. Include the coordinate axes; all the isoclines; all the
equilibrium points; the allowed directions of motion (both vertical and horizontal) in all the regions
into which the isoclines divide the xx plane; direction of motion along isoclines, where applicable.
dx
dt
||
7-y₁
dy
dt
=x-7.
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