Paper 2, Section I, C

Differential Equations | Part IA, 2009

The size of the population of ducks living on the pond of a certain Cambridge college is governed by the equation

dN dt=αNN2\frac{\mathrm{d} N}{\mathrm{~d} t}=\alpha N-N^{2}

where N=N(t)N=N(t) is the number of ducks at time tt and α\alpha is a positive constant. Given that N(0)=2αN(0)=2 \alpha, find N(t)N(t). What happens as tt \rightarrow \infty ?

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