Solve Logistic Equation: Find P(65) | Homework Due Early

[CookieSalesman]

Would really appreciate some help on this. Homework is due really early in the morning tomorrow, and I've been trying at this for a few hours to no avail.

I have a logistic equation, (sorry, I just cannot use latex)
dP/dT = (.00777777)P(9-P)
(For P positive)

Assume P(0)=2
I must find P(65) or t=65
I've solved this many times over and over, and I continuously get different answers. I'm not sure if I'm not even supposed to solve this, but here's what I try-
I separate variables, and try to integrate this equation. Partial fractions, logarithms, etc, then I find C.
I'm not posting the steps because I've done them at least ten times all different, somehow, but perhaps I'm not supposed to be solving for this?

Anyhow I guess I try to find an equation for P(t) without derivatives- I get constants for C like 7/2, 2/7, other random numbers, not once does it ever work out well.This seems simple enough, just integrate the whole thing, but it really is just impossible for me. However one thing I do the same each time through is to separate variables, one side is 1/P(9-P) dP, the other side is 7/900 dt...
After partial fractions, the rest just goes all weird.I have a second problem I hope someone can help with, I just took a picture of the problem...
http://postimg.org/image/tcscajp83/
Yeah, I know it's standard here for the OP to show as much work as possible, but I kid you not I have spent hours on these problems and I cannot understand them. This second problem I cannot even begin to even try.

Help would be much appreciated.

 

[HomogenousCow]

I solved the first equation and I got the solution 9/[3.5 Exp(-7t)+1], at t=65 this is basically 9.

For the second question you have to again solve the logistics equation with K=4300 (The upper case K), and P(0)=300.
After you solve this, you will get P(t)= 12900/[40 Exp(-kt)+3]. Now the question states that the population tripled in the first year, this means that

P(1)=3P(0)=900, so

12900/[40 Exp(-k)+3]=900, this gives k=1.26113