code: def test_linear_ode(self, solver, solution_times_fn):
      if not tf1.control_flow_v2_enabled():
          self.skipTest("b/152464477")
      jacobian_diag_part = tf.constant([-0.5, -1.0], dtype=tf.float64)
      ode_fn = (
          lambda time, state, jacobian_diag_part: jacobian_diag_part
          * state
      )
      initial_time = 0.0
      initial_state = np.float64([1.0, 2.0])
      solver_instance = solver(rtol=_RTOL, atol=_ATOL)
  
      def grad_fn(jacobian_diag_part):
          results = solver_instance.solve(
              ode_fn,
              initial_time,
              initial_state,
              solution_times=solution_times_fn(1.0),
              constants={"jacobian_diag_part": jacobian_diag_part},
          )
          return results.states, results.times
  
      (_, times), grad = tfp_gradient.value_and_gradient(
          grad_fn, jacobian_diag_part, has_aux=True
      )
      times, grad = self.evaluate([times, grad])
  
      def exact_grad_fn(jacobian_diag_part):
          states_exact = (
              tf.exp(
                  jacobian_diag_part[tf.newaxis, :]
                  * times[:, tf.newaxis]
              )
              * initial_state
          )
          return states_exact
  
      _, exact_grad = tfp_gradient.value_and_gradient(
          exact_grad_fn, jacobian_diag_part
      )
      exact_grad = self.evaluate(exact_grad)
      self.assertAllClose(exact_grad, grad, atol=1e-5)
  
imports: from absl.testing import parameterized
  import numpy
  import tensorflow.compat.v1
  import tensorflow.compat.v2
  from tensorflow_probability.python.internal import test_util
  from tensorflow_probability.python.math import gradient
  from tensorflow_probability.python.math.ode import base
  from tensorflow_probability.python.math.ode import bdf
  from tensorflow_probability.python.math.ode import dormand_prince
label_desc: Use image node_id 3 for calling the GradientTest obj's underlying member method code with example usage: obj.test_linear_ode(solver, solution_times_fn) and returns: results,  results, states_exact