Repair ode API after refactor broke it (#3684)

* add DtypeError with informative error message

* use float64 in augment system because of scipy

* set dtypes explicitly in all places

* fix incorrect sensitivity matrix column order
closes #3676
+ order of sensitivity columns now beginning with y0
+ tests were aligned
+ order of y0, theta now everywhere

* more detailed docstrings

* re-run after the fix

* update & re-run after the fix

Author: michaelosthege

docs/source/notebooks/ODE_API_introduction.ipynb

@@ -33,4 +33,13 @@ def __init__(self, message, actual=None, expected=None):
         if expected and actual:
             super().__init__('{} (actual {} != expected {})'.format(message, actual, expected))
         else:
-            super().__init__(message)
+            super().__init__(message)
+
+
+class DtypeError(TypeError):
+    """Error that the dtype of a variable is incorrect."""
+    def __init__(self, message, actual=None, expected=None):
+        if expected and actual:
+            super().__init__('{} (actual {} != expected {})'.format(message, actual, expected))
+        else:
+            super().__init__(message)