6.2. Linearity

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

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

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

(6.4)\[\begin{equation} \vv{y}' = \vv{A} \vv{y} \end{equation}\]

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).