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## Function template integrate

boost::numeric::odeint::integrate — Integrates the ODE.

## Synopsis

    // In header: <boost/numeric/odeint/integrate/integrate.hpp>

    template<typename System, typename State, typename Time, typename Observer>
      boost::enable_if< typename has_value_type< State >::type, size_t >::type
      integrate(System system, State & start_state, Time start_time,
                Time end_time, Time dt, Observer observer);

## Description

Integrates the ODE given by system from start_time to end_time starting with start_state as initial condition and dt as initial time step. This function uses a dense output dopri5 stepper and performs an adaptive integration with step size control, thus dt changes during the integration. This method uses standard error bounds of 1E-6. After each step, the observer is called.

| Note
A second version of this function template exists which explicitly expects the value type as template parameter, i.e. integrate< double >( sys , x , t0 , t1 , dt , obs );

Parameters:

`dt` | Initial step size, will be adjusted during the integration.
`end_time` | End time of the integration.
`observer` | Observer that will be called after each time step.
`start_state` | The initial state.
`start_time` | Start time of the integration.
`system` | The system function to solve, hence the r.h.s. of the ordinary differential equation.

Returns: | The number of steps performed.