# 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:  $dy/dt + p(t)y = f(t)$
• 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

In class