code: def exp_fun_jac(x, y):
      df_dy = np.empty((2, 2, x.shape[0]))
      df_dy[0, 0] = 0
      df_dy[0, 1] = 1
      df_dy[1, 0] = 1
      df_dy[1, 1] = 0
      return df_dy
  
imports: import sys
  import numpy
  from numpy.testing import assert_, assert_array_equal, assert_allclose, assert_equal
  from pytest import raises
  from scipy.sparse import coo_matrix
  from scipy.special import erf
  from scipy.integrate._bvp import modify_mesh, estimate_fun_jac, estimate_bc_jac, compute_jac_indices, construct_global_jac, solve_bvp
label_desc: Use image node_id 2 for calling a global function with example usage: exp_fun_jac(x, y) and returns: df_dy