NAG Library Manual, Mark 30
```/* nag::ad::d02pr Passive Example Program.
*/

#include <dco.hpp>
#include <iostream>

// Function which calls NAG AD routines.
// Solves the problem x''=x/r^3, y''=-y/r^3, with r=sqrt(x^2+y^2) and
// initial conditions x(0)=1-eps, x'(0)=0, y(0)=0, y'(0)=sqrt((1+eps)/(1-eps))
// by solving the ODE system:
//    y1'=y3, y2'=y4, y3'=-y1/r^3, y4'=-y2/r^3
// over the range [0,6*pi].
template <typename T> void func(T &eps, std::vector<T> &y);

int main()
{
std::cout << "nag::ad::d02pr Passive Example Program Results\n\n";

// Parameter epsilon
double eps = 0.7;
// Solution y
std::vector<double> y;

// Call NAG Lib
func(eps, y);

// Print outputs
std::cout.setf(std::ios::scientific, std::ios::floatfield);
std::cout.precision(6);
std::cout << "\n Solution computed with required tolerance " << 1e-4
<< std::endl;
for (std::size_t i = 0; i < y.size(); i++)
{
std::cout << " y" << i + 1 << " = " << y[i] << std::endl;
}
std::cout << std::endl;

return 0;
}

// function which calls NAG AD Library routines
template <typename T> void func(T &eps, std::vector<T> &y)
{
// Active variables
const Integer n = 4, npts = 6;
const Integer liwsav = 130, lrwsav = 350 + 32 * n;

std::vector<T>       thresh(n, 1e-10), ypnow(n), rwsav(lrwsav);
std::vector<Integer> iwsav(liwsav);

// Set parameters for the integrator.
Integer method = -3;
T tol = 1e-4, hstart = 0.0, tnow, tend = 6.0 * nag_math_pi, tstart = 0.0;
T tinc  = (tend - tstart) / ((double)npts);
T twant = tstart + tinc;
// Set initial conditions
y.resize(n);
y[0] = 1.0 - eps;
y[1] = y[2] = 0.0;
y[3]        = sqrt((1.0 + eps) / (1.0 - eps));
// Create AD configuration data object
Integer           ifail = 0;

// Initialize Runge-Kutta method for integrating ODE
ifail = 0;
method, hstart, iwsav.data(), rwsav.data(), ifail);

const T &          t,
const Integer &    n,
const T            y[],
T                  yp[])
{
T r   = 1.0 / sqrt(y[0] * y[0] + y[1] * y[1]);
r     = r * r * r;
yp[0] = y[2];
yp[1] = y[3];
yp[2] = -y[0] * r;
yp[3] = -y[1] * r;
};
do
{
ifail = 0;
// Solve an initial value problem for a 1st order system of ODEs