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x = number of rabbits

y = number of foxes

Accept the usual assumptions involved in predator-prey (Lotka-Volterra) problems.

dx/dt = 0.04x - 0.002xy

dy/dt = -0.08y + 0.0004xy

Initial conditions: 200 rabbits and 10 foxes

This problem is in a textbook. A graph of the functions x and y when 0 </= t </= 240 is illustrated without showing the functions that are graphed. I am trying to generate those functions.

I am having trouble solving the differential equations. I began by separating variables...

dx/dt = 0.04x - 0.002xy

500(1/x)dx = (20 - y)dt

500 ln(x) = t(20 - y) + C1

Using initial conditions, C1 = 500 ln(200), so

500 ln(x) = t(20 - y) + 500 ln(200)

Solving the other equation in a similar way gives

2500 ln(y) = t(x - 200) + 2500 ln(10)

From here I tried several techniques put found myself painted into a corner. I am thinking I need to rethink the method of solving the equations above. Euler's Method may work to approximate values, but I don't know how to set it up. Suggestions?

Thanks for taking a look.

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# Solving Predator-Prey Equations

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