import numpy as np
import math
from scipy.integrate import odeint
import matplotlib.pyplot as plt

def model(y,t):
    dydt = math.cos(t)
    return dydt

initial_conditions = [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5]

t = np.linspace(0,10)

for y0 in initial_conditions:
    y = odeint(model,y0,t)
    plt.plot(t, y, label=f'y(0) = {y0}')

plt.xlabel('time')
plt.ylabel('y(t)')
plt.grid()
plt.legend(loc='upper right')
plt.show()