# Linearity

A system of first-oder ODEs is linear if it can be written in the form:

\begin{equation}
\vv{y}' = \vv{A}(t) \vv{y} + \vv{g}(t)
\end{equation}

Linear systems have unique solutions and special properties we will discuss
later. An important special case is the homogeneous linear system with constant
coefficients:

\begin{equation}
\vv{y}' = \vv{A} \vv{y}
\end{equation}

Note that **A** is now constant and $\vv{g} = \vv{0}$. We will focus on solving
these types of problems because they come up a lot in chemical engineering
analysis (e.g., controls).