Simple Differiential equation, just finding a constant C problem .:Resolved:.

[voidflux]

Hello everyone, I'm close to the solution but i just got hung up on some sort of algebra mistake i think.....

I'm solving a Logistics Equation, dealing with population growth/decay
All i have to do is use P(0) = Po to get C2 and then it will be solved.
Po stands for P sub o. not P*0.

I have

P/(M-P) = C2 e^(mkt)

note: C2 is just a constant C, u get when u integrate.
M and k are constants.

I now the solution is:

P(t) = MPo/[Po + (M-Po)*e^(-kmt)]

Here is what I did,

P/(M-P) = C2*e^(mkt)
P = C2*e^(mkt) (M-P)
now I used P(0) = Po;
Po = C2*e^(mk(0)) (M-P)
C2 = Po/(M-P);
Then i plugged C2 back into the orginal equation and I got
P/(M-P) = [Po/(M-P)]*e^(mkt);

which looks nothing like the solution...any ideas where I messed up?

Thanks for listening!