Verhulst differential equation is usually written: dN/dt=rN(1-N/K) and has the solution N(t)=K/(1+CKe^(-rt)). We have the variables x and y replacing t and N, K=5, r=0.5. So y=5/(1+5Ce^(-0.5x)). C is thus calculated from 1/y(0)-1/K, where the value of y(0) is the initial condition when x=0. C could be incorporated into the exponential as c-0.5x, where c=ln(C).