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int rkqc(double *,double *,int,double *,double,double,double *,
         double *,double *,term *,double *,double **,double,double);
int derivs(term *, int, double, double *, double *, double *, double **);
int odeint( double *ystart, /* ystart[1..n] are the initial values         */
            int nvar,       /* number of dependent variables               */
            double x1,      /* starting value of independent variable      */
            double x2,      /* ending value of independent variable        */
            double eps,     /* accuracy desired                            */
            double h1,      /* guessed first stepsize                      */
            double hmin,    /* minimum allowed stepsize (can be zero)      */
            int *nok,       /* number of good steps taken                  */
            int *nbad,      /* number of bad, but retried and fixed, steps */
            term *f,
            double *xptr,   /* pointer to value of independent variable    */
            double **yptr,  /* array of pointers, dimension nvar,
                               legal indices starting from 1               */
            double xtol,    /* don't make lines more than this long        */
            double ytol
          );
          
int ode(double *ystart, /* ystart[1..n] are the initial values */
        int nvar,    /* number of dependent variables */
        double x1,    /* starting value of independent variable */
        double x2,    /* ending value of independent variable */
        term x,      /* the independent variable */
        term *y,     /* array of dependent variables */
        term *f,    /*  array of symbolic right-hand sides in y' = f(x,y) */
        double eps,   /* accuracy desired */
        double h1,    /* guessed first step size */
        double xtol, /* world coordinates of four pixels in x direction */
        double ytol  /* don't make lines more than four pixels wide or high */
       );
          

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