code: def test_t_eval_dense_output():
      rtol = 1e-3
      atol = 1e-6
      y0 = [1 / 3, 2 / 9]
      t_span = [5, 9]
      t_eval = np.linspace(t_span[0], t_span[1], 10)
      res = solve_ivp(
          fun_rational, t_span, y0, rtol=rtol, atol=atol, t_eval=t_eval
      )
      res_d = solve_ivp(
          fun_rational,
          t_span,
          y0,
          rtol=rtol,
          atol=atol,
          t_eval=t_eval,
          dense_output=True,
      )
      assert_equal(res.t, t_eval)
      assert_(res.t_events is None)
      assert_(res.success)
      assert_equal(res.status, 0)
  
      assert_equal(res.t, res_d.t)
      assert_equal(res.y, res_d.y)
      assert_(res_d.t_events is None)
      assert_(res_d.success)
      assert_equal(res_d.status, 0)
  
      # if t and y are equal only test values for one case
      y_true = sol_rational(res.t)
      e = compute_error(res.y, y_true, rtol, atol)
      assert_(np.all(e < 5))
  
imports: from itertools import product
  from numpy.testing import assert_, assert_allclose, assert_array_less, 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 29 for calling a global function with example usage: test_t_eval_dense_output() without return types