6.2 Linearity

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

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

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).