ODE Review

An ODE is a differential equation of the form

$$\frac{\partial{y}}{\partial{t}} = f(x,y)$$

with initial conditions $y(t=0) = y_0$ where

• $y$ consists of the state variables that are integrated,
• $t$ is the time variable,
• $x$ are the parameters,
• $f$ is the ODE function.

Example

For example, Newton's law of cooling is

$$\frac{\partial{T}}{\partial{t}}= k(T − T_0)$$

where

• $T$ is the scalar state variable that is being integrated,
• $t$ is the time variable,
• $k$ and $T_0$ are parameters,
• $k(T − T_0)$ is the ODE function.