Question Number 7728 by FilupSmith last updated on 13/Sep/16
$$\frac{{dN}}{{dt}}={N}^{{t}} \\ $$$${N}\left({t}\right)=? \\ $$
Commented by sou1618 last updated on 13/Sep/16
$${N}\left({t}\right)=\int{N}^{{t}} {dt} \\ $$$$\:\:\:\:\:\:\:\:=\int{e}^{{t}\:{lnN}} {dt} \\ $$$${u}={t}\:{lnN} \\ $$$${du}={lnNdt} \\ $$$$\:\:\:\:\:\:\:\:=\frac{\mathrm{1}}{{lnN}}\int{e}^{{u}} {du} \\ $$$$\:\:\:\:\:\:\:\:=\frac{\mathrm{1}}{{lnN}}{e}^{{tlnN}} \\ $$$$\:\:\:\:\:\:\:\:=\frac{\mathrm{1}}{{lnN}}{N}^{{t}} \\ $$$$ \\ $$