Differential Equations:
Differential equations give us a dynamic, c.f. static, relationship over time of various types of behaviour (or phenomena) we want to study.
Note that the same differential equation can represent various types of system. For example a second order differential equation of the form shown below:
a2*d2y/dt2 + a1*dy/dt + a0 = 0
could be used to represent any of the following systems:
 | Inductor Capacitor Resistor (LCR) circuit |
| Mass Spring Damper (MSD) mechanism |
| Simple Electro-Hydraulic Actuator (EHA) |
| Longitudinal axis, short period dynamics, of an aircraft |
We should also note that there are different types of differential equation such as:
| linear => dy/dt -y = 0 |
| non linear => dy/dt - y*y = 0 |
| partial => d2u/dt2 = c2(d2u/dx2 + d2u/dy2) |
Usually we try to linearise non linear differential equations which describe the phenomena we want to study.