初始值为负时Runge-Kutta(RK4)算法行为异常问题排查

我实现了用于求解一阶微分方程的C++版RK4算法，代码如下：

using ODE_Function = std::function<double/*dy/dx*/(double/*x*/, double/*y*/)>;

template<int length> //"length" is the number of data points
double* rk4(ODE_Function fxn, double y0, double x0, double h) {

    double* y = new double[length];
    
    y[0] = y0; //initialize output array
    double x = x0; //n is our discretized x variable

    //main loop
    for (int n = 1; n < length; n++) {//y0 is already known, so we start from the second data point
        
        double k1 = fxn(x, y[n-1]);
        double k2 = fxn(x + h/2, y[n-1] + h*k1/2);
        double k3 = fxn(x + h/2, y[n-1] + h*k2/2);
        double k4 = fxn(x + h, y[n-1] + h*k3);

        y[n] = y[n-1] + h/6*(k1 + 2*k2 + 2*k3 + k4);
        x += h;
    }

    return y;
}

但当初始值x0为负时，算法行为异常：理论上以下三个测试案例的结果都应符合(-x²)-2(x+1)的趋势，仅观察窗口不同，但只有最后一个案例符合预期。第一个案例结果呈负指数趋势，第二个案例结果呈正指数趋势，测试代码如下：

测试案例1：x0 = -1 #

double fxn(double x, double y) {
    return x*x + y;
}
int main() {
    const int length = 100;
    double y0 = -2;
    double x0 = -1; //LOOK HERE
    double h = 0.1;

    double* result = rk4<length>(fxn, y0, x0, h);
}

测试案例2：x0 = -5 #

double fxn(double x, double y) {
    return x*x + y;
}
int main() {
    const int length = 100;
    double y0 = -2;
    double x0 = -5; //LOOK HERE
    double h = 0.1;

    double* result = rk4<length>(fxn, y0, x0, h);
}

测试案例3：x0 = 0 #

double fxn(double x, double y) {
    return x*x + y;
}
int main() {
    const int length = 100;
    double y0 = -2;
    double x0 = 0; //LOOK HERE
    double h = 0.1;

    double* result = rk4<length>(fxn, y0, x0, h);
}

内容的提问来源于stack exchange，提问作者Aryan MP