Couple differential equations

Hey guys, Ive been doing some Diffy Q work and I have a few problems I am stuck with. I figured id post up some of the ones Im stuck on and hopefully someone can help. Im having a hard time understanding what is going on with these problems and what they actually mean in words.

1.

$\displaystyle \frac{dP}{dt} = P(1-P); P = \frac{Ce^t}{1 + Ce^t}$

In the problem above a one-paremeter family of solutions of the DE $\displaystyle P' = P(1 - P) $ is given. Does any solution curve pass through the point (0,3)? Through the point (0,1)?

2. Newton's Law of Cooling/Warming

A cup of coffee cools according to Newton's Law of cooling

$\displaystyle \frac{dT}{dt} = K(T-Tm) $

Use date from the graph of the temperature T(t) to estimate the constants Tm, and T0(T naught), and K in a model of the form of a first-order initial-value problem:

$\displaystyle \frac{dT}{dt} = K(T-Tm), T(0) = T0 $

http://i909.photobucket.com/albums/a...andWarming.jpg

Thank you for you help. Im just lost at the terminology of differential equations and what exactly what im trying to be able to understand. Any help is appreciated.