code: def fun_medazko(t, y):
      n = y.shape[0] // 2
      k = 100
      c = 4
  
      phi = 2 if t <= 5 else 0
      y = np.hstack((phi, 0, y, y[-2]))
  
      d = 1 / n
      j = np.arange(n) + 1
      alpha = 2 * (j * d - 1) ** 3 / c**2
      beta = (j * d - 1) ** 4 / c**2
  
      j_2_p1 = 2 * j + 2
      j_2_m3 = 2 * j - 2
      j_2_m1 = 2 * j
      j_2 = 2 * j + 1
  
      f = np.empty(2 * n)
      f[::2] = (
          alpha * (y[j_2_p1] - y[j_2_m3]) / (2 * d)
          + beta * (y[j_2_m3] - 2 * y[j_2_m1] + y[j_2_p1]) / d**2
          - k * y[j_2_m1] * y[j_2]
      )
      f[1::2] = -k * y[j_2] * y[j_2_m1]
  
      return f
  
imports: from itertools import product
  from numpy.testing import assert_, assert_allclose, assert_equal, assert_no_warnings, suppress_warnings
  import pytest
  from pytest import raises
  import numpy
  from scipy.optimize._numdiff import group_columns
  from scipy.integrate import solve_ivp, RK23, RK45, DOP853, Radau, BDF, LSODA
  from scipy.integrate import OdeSolution
  from scipy.integrate._ivp.common import num_jac
  from scipy.integrate._ivp.base import ConstantDenseOutput
  from scipy.sparse import coo_matrix, csc_matrix
label_desc: Use image node_id 10 for calling a global function with example usage: fun_medazko(t, y) and returns: f