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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.