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## Main Question or Discussion Point

I've been trying to solve the Romeo and Juliet problem in differential equations:

Romeo is in love with Juliet, but in our version of the story, Juliet

is a fickle lover. The more Romeo loves her, the more Juliet wants

to run away and hide. But when Romeo gets discouraged and

backs off, Juliet begins to find him strangely attractive. Romeo,

on the other hand, tends to echo her: he warms up when she loves

him, and grows cold when she hates him.

So let R = Romeo's love for Juliet and

let J = Juliet's love for Romeo

Then

[tex] \frac{dR}{dt}=aJ, \frac{dJ}{dt}=-bR [/tex]

How might I solve this pair of differential equations? Is it possible? I have only taken calculus I and II by the way so my knowledge of DE is limited.

Thanks!

NOTE: This isn't for homework, just from a leisure book I'm reading. Some of you might know it!

BiP

Romeo is in love with Juliet, but in our version of the story, Juliet

is a fickle lover. The more Romeo loves her, the more Juliet wants

to run away and hide. But when Romeo gets discouraged and

backs off, Juliet begins to find him strangely attractive. Romeo,

on the other hand, tends to echo her: he warms up when she loves

him, and grows cold when she hates him.

So let R = Romeo's love for Juliet and

let J = Juliet's love for Romeo

Then

[tex] \frac{dR}{dt}=aJ, \frac{dJ}{dt}=-bR [/tex]

How might I solve this pair of differential equations? Is it possible? I have only taken calculus I and II by the way so my knowledge of DE is limited.

Thanks!

NOTE: This isn't for homework, just from a leisure book I'm reading. Some of you might know it!

BiP