test_df.filter(F.col("start").between(pd.to_datetime('2017-04-13'),pd.to_datetime('2017-04-14'))).show()

+--------------------+-----+
|               start|value|
+--------------------+-----+
|2017-04-13 12:00:...|  1.0|
|2017-04-14 00:00:...|  1.1|
+--------------------+-----+