Binding member functions to a function objects suitable for odeint system function is not easy, at least in C++03. The usual way of using __boost_bind does not work because of the forwarding problem. odeint provides two do_step method which only differ in the const specifiers of the arguments and __boost_bind binders only provide the specializations up to two argument which is not enough for odeint.

But one can easily implement the according binders themself:

template< class Obj , class Mem >
class ode_wrapper
{
    Obj m_obj;
    Mem m_mem;

public:

    ode_wrapper( Obj obj , Mem mem ) : m_obj( obj ) , m_mem( mem ) { }

    template< class State , class Deriv , class Time >
    void operator()( const State &x , Deriv &dxdt , Time t )
    {
        (m_obj.*m_mem)( x , dxdt , t );
    }
};

template< class Obj , class Mem >
ode_wrapper< Obj , Mem > make_ode_wrapper( Obj obj , Mem mem )
{
    return ode_wrapper< Obj , Mem >( obj , mem );
}

One can use this binder as follows

struct lorenz
{
    void ode( const state_type &x , state_type &dxdt , double t ) const
    {
        dxdt[0] = 10.0 * ( x[1] - x[0] );
        dxdt[1] = 28.0 * x[0] - x[1] - x[0] * x[2];
        dxdt[2] = -8.0 / 3.0 * x[2] + x[0] * x[1];
    }
};

int main( int argc , char *argv[] )
{
    using namespace boost::numeric::odeint;
    state_type x = {{ 10.0 , 10.0 , 10.0 }};
    integrate_const( runge_kutta4< state_type >() , make_ode_wrapper( lorenz() , &lorenz::ode ) ,
                     x , 0.0 , 10.0 , 0.01 );
    return 0;
}

namespace pl = std::placeholders;

state_type x = {{ 10.0 , 10.0 , 10.0 }};
integrate_const( runge_kutta4< state_type >() ,
                 std::bind( &lorenz::ode , lorenz() , pl::_1 , pl::_2 , pl::_3 ) ,
                 x , 0.0 , 10.0 , 0.01  );