First order linear DEs, separable DEs

Learning objectives

Work with models using 1st order linear equations
Solve equations that can be put in the form $a(y)dy = b(t)dt$
Recognize 1st order linear DEs:
- undriven (aka homogeneous) if $f(t) = 0$ , otherwise driven
Solve 1st order linear DEs
- $y(t) = Cy_u(t) + y_d(t)$ where
- $y_u$ and $y_d$ are ANY single solutions ( $y_u \ne 0$ ) of the undriven ( $y^\prime + py = 0$ ) and driven ( $y^\prime + py = f$ ) DEs
Find $y_u$ and $y_d$
Uniqueness and existence theorems for 1st order linear DEs