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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?

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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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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