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(a) Show that solution trajectories on the boundary of the square with vertices (-2, –2), (-2, 2), (2, –2) and (2, 2) are directed into the interior of the square (consider each edge separately). (b) Show that r' > 0 for some appropriate value of the polar coordinate r. (Note that it won't be necessary to deal with the o equation.) (c) What do the results of parts (a) and (b) tell you about the existence of a periodic solution?

(a) Show that solution trajectories on the boundary of the square with vertices (-2, –2), (-2, 2), (2, –2) and (2, 2) are directed into the interior of the square (consider each edge separately). (b) Show that r' > 0 for some appropriate value of the polar coordinate r. (Note that it won't be necessary to deal with the o equation.) (c) What do the results of parts (a) and (b) tell you about the existence of a periodic solution?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 17EQ
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3. Consider the system = r - y - a y = x+y – y3 (a) Show that solution trajectories on the boundary of the square with vertices (-2, –2), (-2, 2), (2, –2) and (2, 2) are directed into the interior of the square (consider each edge separately). (b) Show that r' > 0 for some appropriate value of the polar coordinate r. (Note that it won't be necessary to deal with the O' equation.) (c) What do the results of parts (a) and (b) tell you about the existence of a periodic solution?
Transcribed Image Text:3. Consider the system = r - y - a y = x+y – y3 (a) Show that solution trajectories on the boundary of the square with vertices (-2, –2), (-2, 2), (2, –2) and (2, 2) are directed into the interior of the square (consider each edge separately). (b) Show that r' > 0 for some appropriate value of the polar coordinate r. (Note that it won't be necessary to deal with the O' equation.) (c) What do the results of parts (a) and (b) tell you about the existence of a periodic solution?
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