demo, MySQL - rextester

Language: Layout:

#MySQL 5.7.12
#please drop objects you've created at the end of the script 
#or check for their existance before creating
#'\\' is a delimiter

DROP TABLE IF EXISTS yourTable;
CREATE TABLE yourTable (date_column datetime);
INSERT INTO yourTable (date_column)
VALUES
    ('2017-03-01'),
    ('2017-03-02'),
    ('2017-03-03'),
    ('2017-03-04'),
    ('2017-03-05'),
    ('2017-03-06'),
    ('2017-03-07'),
    ('2017-03-08'),
    ('2017-03-09'),
    ('2017-03-10'),
    ('2017-03-11'),
    ('2017-03-12'),
    ('2017-03-13'),
    ('2017-03-14'),
    ('2017-03-15'),
    ('2017-03-16'),
    ('2017-03-17'),
    ('2017-03-18'),
    ('2017-03-19'),
    ('2017-03-20'),
    ('2017-03-21'),
    ('2017-03-22'),
    ('2017-03-23'),
    ('2017-03-24'),
    ('2017-03-25'),
    ('2017-03-26'),
    ('2017-03-27'),
    ('2017-03-28'),
    ('2017-03-29'),
    ('2017-03-30'),
    ('2017-03-31');

SELECT date_column
FROM yourTable
WHERE (date_column BETWEEN '2017-03-01' AND '2017-03-31' AND
       DAYOFWEEK(date_column) = 1) OR
      date_column = '2017-03-31';


absolute service time: 0,32 sec