#058

import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(-6, 6, 800)
constants = [0.2, 0.5, 1, 2, 5, 10]

fig, ax = plt.subplots(figsize=(7, 4.5))

for constant in constants:
    y = 1 / (constant * np.exp(-x) + 1)
    ax.plot(x, y, linewidth=2, label=f"C = {constant}")

ax.axhline(0, color="#111827", linewidth=1, alpha=0.55, label="equilibrium y = 0")
ax.axhline(1, color="black", linewidth=1, alpha=0.7, label="stable equilibrium y = 1")
ax.axvline(0, color="#111827", linewidth=0.8, alpha=0.35)
ax.set_title("Entry #058: y' = y(1 - y)")
ax.set_xlabel("x")
ax.set_ylabel("y")
ax.set_ylim(-0.2, 1.2)
ax.grid(True, alpha=0.3)
ax.legend(fontsize=8, ncols=2)

fig.tight_layout()
plt.show()