import matplotlib.pyplot as plt


def euler(f, n: int, delta_x: float, x_0: float, y_0: float) -> list[float]:
    results = []

    x = x_0
    y = y_0
    for i in range(n):
        x = x + delta_x
        y = y + delta_x * f(x, y)
        results.append(y)

    return results


def exercice1() -> None:
    f = lambda x, y: -2 * x * y + 1
    results = euler(f, n=20, x_0=0, y_0=1, delta_x=.2)
    plt.plot(results)
    plt.title('Euler')
    plt.show()


if __name__ == '__main__':
    exercice1()