10.5: Applications and modeling.

Main Points
For the differential equation: dy/dx = k(y - A) the general solution is y = A + Ce^kt for any constant C. An equilibrium solution is constant for all the values of the independent variable, at this point the graph of the solution is a horizontal line. This solution is stable when a change in the initial conditions produces a solution that heads towards the equilibrium as the independent variable heads towards positive infinity and is unstable when the solution of the initial conditions veeraway from the equilibrium. A differential equation may have more than one equilibrium.
Newton proposed that the temp of a hot object decreases at a rate proportional to the difference between it and the surroundings and the same with cold objects.

Challenges
I feel as though the book is too specific with its examples and thus understanding the topic outside the example is a little difficult. Obtaining the general solution is fairly easy when we are given the differential equation is given. How do we do anything else with it? And why are there a number of graphs for a solution? Do all differential equations have equilibrium solutions?
(I think I really need to go over that class I missed with you)