## 13.1 Notation

An ODE is defined by a set of differential equations, $$y(t, \theta)' = f(t, y, \theta)$$, and initial conditions, $$y(t_0, \theta) = y_0$$. The function $$f(t, y, \theta)$$ is called the system function. The $$\theta$$ dependence is included in the notation for $$y(t, \theta)$$ and $$f(t, y, \theta)$$ as a reminder that the solution is a function of any parameters used in the computation.