Explain the product of infected and susceptible proportions

Find the general solution of $dy/dt=ky(1-y)$, $0<y<1$, $k>0$, in the form $y=f(t)$.3 marks

Find the particular solution with $y(0)=1/4$, and sketch it.3 marks

Here $y$ models the proportion infected by a disease. Explain why the differential equation may be suitable.2 marks