Gompertz differential equation proof

• Oct 8th 2010, 07:37 AM
Warrenx
Gompertz differential equation proof
I have no idea what this question is asking me:

27. Show that $y = Me^{ae^{kt}}$ is a solution for any constant a.

it gives me this hint:
dy/dt = ky ln(y/m).

I would assume that because it is an exponent that any constant for a would give a definable solution.
I do not know what it is I am trying to prove or what is going on, any help would be appreciated.

Thanks.
• Oct 8th 2010, 09:50 AM
emakarov
I think that this problem is given in a context that deals with the Gompertz differential equation. You have not provided this equation, so it is not clear a solution to what is being discussed.
• Oct 8th 2010, 01:14 PM
Ackbeet
$y=Me^{ae^{kt}},$ its derivative is
$y'=Me^{ae^{kt}}(ae^{kt})k.$
$ky\ln(y/M)=kMe^{ae^{kt}}\ln(e^{ae^{kt}})=kMe^{ae^{kt}}(ae^ {kt}).$