code: def test_classes():
      y0 = [1 / 3, 2 / 9]
      for cls in [RK23, RK45, DOP853, Radau, BDF, LSODA]:
          solver = cls(fun_rational, 5, y0, np.inf)
          assert_equal(solver.n, 2)
          assert_equal(solver.status, "running")
          assert_equal(solver.t_bound, np.inf)
          assert_equal(solver.direction, 1)
          assert_equal(solver.t, 5)
          assert_equal(solver.y, y0)
          assert_(solver.step_size is None)
          if cls is not LSODA:
              assert_(solver.nfev > 0)
              assert_(solver.njev >= 0)
              assert_equal(solver.nlu, 0)
          else:
              assert_equal(solver.nfev, 0)
              assert_equal(solver.njev, 0)
              assert_equal(solver.nlu, 0)
  
          assert_raises(RuntimeError, solver.dense_output)
  
          message = solver.step()
          assert_equal(solver.status, "running")
          assert_equal(message, None)
          assert_equal(solver.n, 2)
          assert_equal(solver.t_bound, np.inf)
          assert_equal(solver.direction, 1)
          assert_(solver.t > 5)
          assert_(not np.all(np.equal(solver.y, y0)))
          assert_(solver.step_size > 0)
          assert_(solver.nfev > 0)
          assert_(solver.njev >= 0)
          assert_(solver.nlu >= 0)
          sol = solver.dense_output()
          assert_allclose(sol(5), y0, rtol=1e-15, atol=0)
  
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 36 for calling a global function with example usage: test_classes() without return types