Past exam of the mathematics course of the University of Cambridge / 2005 / ii / Paper 3 / 6E / a / Solution

The probability of an exact copy is $Q=q^L$. Incorrect copies contribute mutants at rate $a(1-Q)x$, giving $\boxed{\dot{y}=by+a(1-Q)x}$. For $y>0$, differentiating the ratio givesThis is a logistic-type equation for relative concentration; the absolute concentrations need not have a stationary value.