Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 3 / 6A / c

Set $\omega =\pi /(2\tau )$. The condition $r\tau =-\pi /2$ says $r=-\omega$. ThensatisfiesIt is periodic with period $2\pi /\omega =4\tau$. Every nonzero such solution is negative during half of each period, so it cannot represent a population size.