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.

For example, FriCAS appears to give a wrong answer for this.

@ldbeth how much memory does it have? it really looks impressive nevertheless.

@ldbeth wow, really mind-blowing. i can't imagine the optimization done on it.

@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

@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)

Results in:

P = %e^(log(c)*%e^-(b*t)-(a*%e^-(b*t))/b+a/b)

@loke It just factors out (log c - a/b), so it is equivalent to Voyage 200's result.

@ldbeth i have not performed any checks but, are you sure? maybe they are actually equal?

@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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