Exercise 11.59 Let m(t ) be the expected size at time t of the population in a birthdeath process with birth rate and death

Exercise 11.59 Let m(t ) be the expected size at time t of the population in a birth–death process with birth rate λ and death rate μ. Use (11.55) to show that m satisfies the differential equation m′(t ) = (λ − μ)m(t ).

Hence find m(t) in terms of the initial size of the population.