1. The problem statement, all variables and given/known data A carrier of an infectious disease joins a herd of 500 initially uninfected cattle. At any instant in time, the rate at which the disease spreads dx/dt is known to be proportional to the product of: (i) the number of infected cattle x(t); and (ii) the number of uninfected cattle. If the number of cattle infected after 4 days is 50, how many will have been infected after 6 days? 2. Relevant equations 3. The attempt at a solution I interpreted the problem as the following D.E: dx/dt=k*x*(500-x); where k is a constant to be determined And the initial condition: x(0)=0 And the given information: x(4)=50 The equation looks to be separable: dx/(500*k*x-k*x^(2)) = dt but I cannot integrate the left hand side. Is my interpreted D.E correct? If yes how to integrate the left hand side? Appreciate your help.