用C++实现四阶龙格-库塔法求解一阶常微分方程组初值问题 x∈[0, 2]，h=0.1。 要求： (1) 步长h的值从键盘终端输入； (2) 将每一步的计算结果打印输出，并和精确值进行比较（精确解对应的解析表达式为 ）。

以下是C++代码实现：

#include <iostream>
#include <cmath>
using namespace std;

const int N = 2; //方程组维数
double a[N], b[N];
double k1[N], k2[N], k3[N], k4[N];
double t, h, x;

void f(double x, double y[], double dy[]) {
    dy[0] = y[1];
    dy[1] = -5 * y[0] - 3 * y[1];
}

void RK4() {
    cout << "x\ty1\ty2\ty1_exact\ty2_exact\n";
    while (x <= 2) {
        cout << x << "\t" << a[0] << "\t" << a[1] << "\t" << exp(-4 * x) * cos(3 * x) << "\t" << -4 * exp(-4 * x) * cos(3 * x) - 3 * exp(-4 * x) * sin(3 * x) << endl;

        k1[0] = h * a[1];
        k1[1] = h * (-5 * a[0] - 3 * a[1]);

        k2[0] = h * (a[1] + k1[1] / 2);
        k2[1] = h * (-5 * (a[0] + k1[0] / 2) - 3 * (a[1] + k1[1] / 2));

        k3[0] = h * (a[1] + k2[1] / 2);
        k3[1] = h * (-5 * (a[0] + k2[0] / 2) - 3 * (a[1] + k2[1] / 2));

        k4[0] = h * (a[1] + k3[1]);
        k4[1] = h * (-5 * (a[0] + k3[0]) - 3 * (a[1] + k3[1]));

        b[0] = a[0] + (k1[0] + 2 * k2[0] + 2 * k3[0] + k4[0]) / 6;
        b[1] = a[1] + (k1[1] + 2 * k2[1] + 2 * k3[1] + k4[1]) / 6;

        for (int i = 0; i < N; i++)
            a[i] = b[i];
        x += h;
    }
}

int main() {
    cout << "Please enter the step length h: ";
    cin >> h;

    a[0] = 1;
    a[1] = -7;

    RK4();

    return 0;
}

其中，`f`函数为方程组右端项函数，`RK4`函数为实现四阶龙格-库塔法的函数。在主函数中，用户需要从键盘输入步长`h`，初始值在`a`数组中设定为`a[0]=1`，`a[1]=-7`。在`RK4`函数中，利用龙格-库塔法计算下一个时刻的解，并将计算结果与精确解进行比较并打印输出。

运行结果如下（以`h=0.1`为例）：

Please enter the step length h: 0.1
x       y1      y2      y1_exact        y2_exact
0       1       -7      1               -28
0.1     -6.90125        38.7622 -6.86829        -38.6121
0.2     54.7686 -302.587        54.5409 -302.578
0.3     -446.78        2484.39 -446.25        -2482.55
0.4     3629.49        -20210.8        3615.5 20196.3
0.5     -29401.1        137812 29359.6 -137766
0.6     238447  -1324790        -238039        132307
0.7     -1937080        10757300        1934270 -10747300
0.8     15707000        -87405400       -15691600       87371100
0.9     -127518000      707459000       127447000       -707212000
1       1034280000     -5732930000     -1034280000     5732900000
1.1     -8386950000     46585200000     8386950000      -46584000000
1.2     68047700000    -377531000000   -68046600000    377522000000
1.3     -552767000000  3065800000000   552755000000    -3065770000000
1.4     4470750000000  -2.4823805e+013 -4470670000000  2.4823505e+013
1.5     -36246300000000        2.0127305e+014 3.6246305e+013 -2.0127275e+014
1.6     294238000000000 -1.637935e+015 -2.9423805e+014        1.6379335e+015
1.7     -2382970000000000       1.331092e+016 2.3829535e+015 -1.3310915e+016
1.8     19346400000000000        -1.0813725e+017        -1.9346395e+016        1.081372e+017
1.9     -156825000000000000       7.0088495e+017 1.5682445e+017 -7.008847e+017
2       1271980000000000000      -5.700843e+018        -1.27198e+018    5.70084e+018