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R(t) = Romeo's love/hate for Juliet at time t J(t) = Juliet's love/hate for Romeo at time t What happens when romantic opposites get together? A model for their romance is R = aJ j= -bR + aj, a and b positive e. If 4b = a i. Write the general solution. ii. Classify the origin.

R(t) = Romeo's love/hate for Juliet at time t J(t) = Juliet's love/hate for Romeo at time t What happens when romantic opposites get together? A model for their romance is R = aJ j= -bR + aj, a and b positive e. If 4b = a i. Write the general solution. ii. Classify the origin.

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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Love Affairs (Strogatz, Nonlinear Dynamics and Chaos, 1994) Let R(t) = Romeo's love/hate for Juliet at time t J(t) = Juliet's love/hate for Romeo at time t What happens when romantic opposites get together? A model for their romance is R = aJ j=-bR+aJ, a and b positive e. If 4b = a i. Write the general solution. ii. Classify the origin. iii. Summarize what happens in their relationship. (Hint: Think about the eigenvectors. Be sure to consider all the qualitatively different possibilities.)
Transcribed Image Text:Love Affairs (Strogatz, Nonlinear Dynamics and Chaos, 1994) Let R(t) = Romeo's love/hate for Juliet at time t J(t) = Juliet's love/hate for Romeo at time t What happens when romantic opposites get together? A model for their romance is R = aJ j=-bR+aJ, a and b positive e. If 4b = a i. Write the general solution. ii. Classify the origin. iii. Summarize what happens in their relationship. (Hint: Think about the eigenvectors. Be sure to consider all the qualitatively different possibilities.)
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Summarize what happens in their relationship. (Hint: Think about the eigenvectors. Be sure to consider all the qualitatively different possibilities.)

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