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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.