Итерационный метод Эйлера

from itertools import zip_longest
import numpy as np
import matplotlib.pyplot as plt
import mplcyberpunk
from prettytable import PrettyTable, SINGLE_BORDER
import sympy as sym
def foo(x, y, beta):
    return -y**2 + (beta*x)/(1+x**2)
 
 
def iter_euler(f, x0, y0, a, b, h=0.1, eps=1e-4):
    n = int((b - a)/h)
    y = y0
    ys = [y0]
    for i in range(n):
        flag = True
        yk = y + f(x0 + h * i, y, beta)
        while flag:
            y_place_holder = yk
            yk = y + (f(x0 + h * i, y, beta) + f(x0 + h*(i+1), yk, beta)) * h / 2
            if abs(yk - y_place_holder) < eps:
                flag = False
                y = yk
                ys.append(y)
                continue
    return ys
 
 
def graphic_mod_euler(a=0, b=1, h=0.1, x0=0, y0=-0.4122, eps=1e-4):
    fig, ax = plt.subplots(figsize=(12, 6))
    betan = [round(2.5+alpha/40, 4) for alpha in range(34, 38)]
    sol = {}
    for index, beta in enumerate(betan):
        sol[index+34] = iter_euler(foo, x0, y0, a, b, h=h, eps=eps)
    for item in sol.items():
        print(item)
    xs = np.arange(a, b+h, h)
    for value in sol.values():
        plt.plot(xs, value)
    plt.grid(which='both', linewidth=1.5, linestyle='-', color='gray')
    ax.tick_params(which='major', length=8, width=2)
    ax.tick_params(which='minor', length=8, width=2)
    ax.minorticks_on()
    ax.grid(which='major',
            linewidth=2)
    ax.grid(which='minor',
            linestyle=':')
    plt.title("'Approximate and Exact Solution for Simple ODE'")
    plt.xlabel("x")
    plt.ylabel("y")
    legend = plt.legend([f'{alpha=}' for alpha in range(34, 38)], title='Legend',
                        loc='upper left', shadow=True, fontsize='x-large',
                        frameon=True, title_fontsize=15, framealpha=1)
    frame = legend.get_frame()
    frame.set_facecolor('black')
    frame.set_edgecolor('red')
    mplcyberpunk.add_glow_effects()
    mplcyberpunk.add_gradient_fill(alpha_gradientglow=0.5)
    plt.show()
    fig.savefig('Euler_iter.png', dpi=300, bbox_inches='tight')
 
 
graphic_mod_euler()