#经典R-K，龙格-库塔法
def ClassicRK(x0,y0,h,xk,fxy):
    k1=k2=k3=k4=0
    result = [(x0,y0)]
    while x0<=xk:
        k1 = fxy(x0,y0)
        k2 = fxy(x0+h/2,y0+h*k1/2)
        k3 = fxy(x0+h/2,y0+h*k2/2)
        k4 = fxy(x0+h,y0+h*k3)
        y0 += h*(k1+4*k2+k3)/6
        x0 += h
        result.append((x0,y0))
    return result

#把下面参数换成题干的#################
if __name__=="__main__":
    x0 = 0   #x的左边界换成题干里面的#################
    y0 = -1  #y的初始值换成题干里面的#################
    fxy = lambda x,y: x + y    #f(x,y)换成题干里面的#################
    real_fx = lambda x: -x-1     #真实函数换成题干里面的#################
    h = 0.1         #步长换成题干里面的#################
    xk = 2           #x的右边界换成题干里面的#################
    result = ClassicRK(x0, y0, h, xk, fxy)
    print("x\ty\t\treal_y\t\t\t误差")
    for x, y in result:
        print(f"{x:.2f}\t{y:.10f}\t\t{real_fx(x):.10f}\t\t\t{abs(y - real_fx(x)):.5f}")