Chasing Ducks: Solving a Differential Equation in a Square Pen

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SUMMARY

The discussion centers on solving a differential equation related to the movement of ducks in a 2m x 2m square pen, where each duck chases its anticlockwise neighbor. The governing differential equation is established as dy/dx = (x-y)/(2-x-y), with the initial condition for the duck in the lower left corner being (0,0). The problem emphasizes the need to derive expressions for dx/dt and dy/dt to further analyze the ducks' trajectories.

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Homework Statement



one duck is situated in each of the four corners of a 2mx2m square pen. suddenly, each duck begins to chase its anticlockwise neighbour. all the ducks travel at the same speed.

(a) by defining the origin of an x-y coordinate system in the bottom left hand corner of the paddock, show that the differential equation governing the path of the duck is dy/dx = (x-y)/(2-x-y); where (x,y) represents the position of the duck starting in the lower left corner.
what is the initial condition for the position of this duck.

The Attempt at a Solution



I have attached the file which shows the ducks in the four corners. I've also added a circle inside the square pen which represents the path of the ducks (not sure if this is right). I don't know where to go from here. I know I have to find expressions for dy/dt and dx/dt then use dy/dt=(dy/dx)*(dx/dt) to find dy/dx but I don't know how to find dx/dt and dy/dt?
Please help. It's revision for an exam!
Thanks
 

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the mighty ducks …

Hi Anabelle! :smile:

hmm … this is a drawing problem, rather than a calculus one

hint: if home duck is at (x,y), where is first duck? :wink:
 

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