I have no idea how this thing gives this accurate result without memory overflow. For desktop computers only a few CAS program can do this.
@loke The highlighted part is the full implicit solution to the differential equation dP/dt = P(a-b*ln(P)) with initial condition P(0)=c, the next part solves the result to equation P = e^((ln c-a/b)*e^(-bt)-a/b) with some conditions. The result is known as the Gompertz Differential Equation, see https://math.stackexchange.com/questions/2450994/solution-to-gompertz-differential-equation
@ldbeth My calculus is pretty bad, so I'm not sure if the solution Maxima gives me is equivalent:
solve(ic1(ode2('diff(P,t) = P*(a-b*log(P)), P, t), t=0, P=c), P)
P = %e^(log(c)*%e^-(b*t)-(a*%e^-(b*t))/b+a/b)
@oneofvalts Welp FriCAS uses a somewhat awkward mechanism for ODE, that the function symbol needs to be constructed differently. I took the result as an equation meaning XXX = 0 and try solve it and it turns out the result should be correct.
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