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1.1:  

Equilibrium Solution

Graphed slope field of ${dv \over dt} = f(t, v)$

*** can use slope field to determine behavior of $v$ including as $t 
\rightarrow \infty$.

1.2:

Solved ${dy \over dt} = a(y - {b \over a})$

Solution:  $y = {b \over a} + ce^{at}$

Initial Value Problem:  $y(0) = y_0$

$t = 0, y = y_0$, then $c = y_0 - {b \over a}$

1.3:

ODE vs PDE

order of differential eq'n:  order of highest derivative

example of order $n$:  $y^{(n)} = f(t, y, ..., y^{(n-1)})$

Linear vs Non-linear

linear:  $a_0(t) y^{(n)} + ... + a_n(t)y = g(t)$

Existence and Uniqueness of Solutions
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CH 2:  Solve ${dy \over dt} = f(t, y)$

2.1:  First order linear eqn:  ${dy \over dt} + p(t)y = g(t)$

Ex 1:  $2{dy \over dt} + 10y = 16$


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