Mathematics & Science Learning Center
Computer Laboratory

Applications of Differential Equations

Population Dynamics

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Your result, rather shockingly, was:

FindRoot[{(verhulst/.t->110)==75.99,
(verhulst/.t->210)==281.4},
{a, 0.02}, {b, 0.01}]

FindRoot::jsing:
Encountered a singular Jacobian at the point {a,b} = {9.4661,3.92068}. Try perturbing the initial point(s). >>

An error message. We must be off by quite a bit with our guesses, and if we look at where Mathematica abandoned its search, the values it has found for a and b are quite ridiculous! I suspect it's our guess for the b value which is leading things astray. We made it half of the a value, but that still seems high for a competition parameter. Let's shrink it by a factor of 10 to b = 0.001, leaving the a value the same.

Go ahead, make this change and do the FindRoot again.

Let's go look at what you should have gotten...

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