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of a physical system is modeled using ODEs, embedded in a conceptual model. The time response of a physical system depends on its initial state. The problem of solving the ODEs for a given initial state is called the initial value problem.

In very few cases these ODEs can be solved in a simple analytic way. More common are ODEs which do not have an analytic solution. In these cases one has to use numerical approximation procedures.

Two well known families of

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