7

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

def system_of_equations(variables, t):
    x, y, dxdt, dydt = variables
    d2xdt2 = x**2 + y**2
    d2ydt2 = x - np.cos(y)**2 + t
    return [dxdt, dydt, d2xdt2, d2ydt2]


initial_conditions = [2, 10, 1, 3]

t_span = np.linspace(0, 1, 1000)

solution = odeint(system_of_equations, initial_conditions, t_span)

x_values = solution[:, 0]
y_values = solution[:, 1]

plt.plot(t_span, x_values, label='x(t)')
plt.plot(t_span, y_values, label='y(t)')
plt.legend()
plt.grid()
plt.title('Розв\'язок системи диференціальних рівнянь')
plt.show()