diff --git a/GPy/kern/constructors.py b/GPy/kern/constructors.py
index 500ab92f..05eaa028 100644
--- a/GPy/kern/constructors.py
+++ b/GPy/kern/constructors.py
@@ -150,33 +150,6 @@ def white(input_dim,variance=1.):
     part = parts.white.White(input_dim,variance)
     return kern(input_dim, [part])
 
-def eq_ode1(output_dim, W=None, rank=1,  kappa=None, length_scale=1., decay=None, delay=None):
-    """Covariance function for first order differential equation driven by an exponentiated quadratic covariance.
-
-    This outputs of this kernel have the form
-    .. math::
-       \frac{\text{d}y_j}{\text{d}t} = \sum_{i=1}^R w_{j,i} f_i(t-\delta_j) +\sqrt{\kappa_j}g_j(t) - d_jy_j(t)
-
-    where :math:`R` is the rank of the system, :math:`w_{j,i}` is the sensitivity of the :math:`j`th output to the :math:`i`th latent function, :math:`d_j` is the decay rate of the :math:`j`th output and :math:`f_i(t)` and :math:`g_i(t)` are independent latent Gaussian processes goverened by an exponentiated quadratic covariance.
-    
-    :param output_dim: number of outputs driven by latent function.
-    :type output_dim: int
-    :param W: sensitivities of each output to the latent driving function. 
-    :type W: ndarray (output_dim x rank).
-    :param rank: If rank is greater than 1 then there are assumed to be a total of rank latent forces independently driving the system, each with identical covariance.
-    :type rank: int
-    :param decay: decay rates for the first order system. 
-    :type decay: array of length output_dim.
-    :param delay: delay between latent force and output response.
-    :type delay: array of length output_dim.
-    :param kappa: diagonal term that allows each latent output to have an independent component to the response.
-    :type kappa: array of length output_dim.
-    
-    .. Note: see first order differential equation examples in GPy.examples.regression for some usage.
-    """
-    part = parts.eq_ode1.Eq_ode1(output_dim, W, rank, kappa, length_scale, decay, delay)
-    return kern(2, [part])
-
 
 def exponential(input_dim,variance=1., lengthscale=None, ARD=False):
     """
diff --git a/GPy/kern/kern.py b/GPy/kern/kern.py
index f021dc3a..46bb01c8 100644
--- a/GPy/kern/kern.py
+++ b/GPy/kern/kern.py
@@ -747,7 +747,7 @@ class Kern_check_model(Model):
         if kernel==None:
             kernel = GPy.kern.rbf(1)
         if X==None:
-            X = np.random.randn(num_samples, kernel.input_dim)
+            X = np.random.normal(size=(num_samples, kernel.input_dim))
         if dL_dK==None:
             if X2==None:
                 dL_dK = np.ones((X.shape[0], X.shape[0]))
@@ -844,7 +844,7 @@ class Kern_check_dKdiag_dX(Kern_check_model):
     def _set_params(self, x):
         self.X=x.reshape(self.X.shape)
 
-def kern_test(kern, X=None, X2=None, output_ind=None, verbose=False):
+def kern_test(kern, X=None, X2=None, output_ind=None, verbose=False, X_positive=False):
     """This function runs on kernels to check the correctness of their implementation. It checks that the covariance function is positive definite for a randomly generated data set.
 
     :param kern: the kernel to be tested.
@@ -858,12 +858,16 @@ def kern_test(kern, X=None, X2=None, output_ind=None, verbose=False):
     pass_checks = True
     if X==None:
         X = np.random.randn(10, kern.input_dim)
+        if X_positive:
+            X = abs(X)
         if output_ind is not None:
-            X[:, output_ind] = np.random.randint(kern.output_dim, X.shape[0])
+            X[:, output_ind] = np.random.randint(kern.parts[0].output_dim, X.shape[0])
     if X2==None:
         X2 = np.random.randn(20, kern.input_dim)
+        if X_positive:
+            X2 = abs(X2)
         if output_ind is not None:
-            X2[:, output_ind] = np.random.randint(kern.output_dim, X2.shape[0])
+            X2[:, output_ind] = np.random.randint(kern.parts[0].output_dim, X2.shape[0])
 
     if verbose:
         print("Checking covariance function is positive definite.")
diff --git a/GPy/testing/kernel_tests.py b/GPy/testing/kernel_tests.py
index 92cad687..5d2fbeec 100644
--- a/GPy/testing/kernel_tests.py
+++ b/GPy/testing/kernel_tests.py
@@ -36,12 +36,12 @@ class KernelTests(unittest.TestCase):
     def test_eq_sympykernel(self):
         if SYMPY_AVAILABLE:
             kern = GPy.kern.eq_sympy(5, 3)
-            self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose))
+            self.assertTrue(GPy.kern.kern_test(kern, output_ind=3, verbose=verbose))
 
-    def test_eq_ode1kernel(self):
+    def test_ode1_eqkernel(self):
         if SYMPY_AVAILABLE:
-            kern = GPy.kern.eq_ode1(3)
-            self.assertTrue(GPy.kern.kern_test(kern, verbose=verbose))
+            kern = GPy.kern.ode1_eq(3)
+            self.assertTrue(GPy.kern.kern_test(kern, output_ind=1, verbose=verbose, X_positive=True))
 
     def test_rbf_invkernel(self):
         kern = GPy.kern.rbf_inv(5)