// PROGRAM example

#include "TrueBASIC.h"
int main();
void initial(double *y, double *x, double *delta_x, double *xmax);
void Euler(double *y, double *x, double delta_x);

int main()                                  // beginning of main program
{
    double delta_x, x, xmax, y;

    // specify initial values and parameters
    initial(&y, &x, &delta_x, &xmax);
    while(x <= xmax)
    {
        Euler(&y, &x, delta_x);             // use simple Euler algorithm
        printf("%12f %12f\n", x, y);
    }

    return 0;
}                                           // end of main program

void initial(double *y, double *x, double *delta_x, double *xmax)
{
    (*x) = 1;                               // initial value of x
    (*y) = 1;                               // initial value of y
    (*xmax) = 2;                            // maximum value of x
    (*delta_x) = 0.1;                       // step size
    printf("          x            y \n");  // print heading
    printf("\n");                           // skip line
    printf("%12f %12f\n", (*x), (*y));      // print initial values
}

void Euler(double *y, double *x, double delta_x)
{
    double change, slope;

    // variables slope and change introduced for sake of clarity only
    slope = 2*(*x);                         // slope at beginning of interval
    change = slope*delta_x;                 // estimate of change during interval
    (*y) += change;                         // new value of y
    (*x) += delta_x;                        // value of x at end of interval
}