I had this problem myself and I fixed it by going to the Microsoft SQL Server management studio and manually connecting the database to the user account you login into the database with.
To do this:

• Open Microsoft SQL Server management studio and connect to your server.
• Go to login, right click on the correct user, and go to properties.
• On the top left there's a panel (titled "select a page"). Go to User mapping.
• On the table displayed, where it says user (second column), type in the name of the user next to the database you are using.

While you are at it, look at the panel at the bottom. Where it says Database role membership for:{database name} , make sure you have db_datareader and db_datawriter checked.

Here is a way to have a connection string using sqlalchemy (see https://www.sqlalchemy.org/ ):

from sqlalchemy import create_engine
from sqlalchemy.orm import sessionmaker
from db import Db

#Get localhost DB
engine = create_engine('mssql+pyodbc://myDbUser:myDbPassword@localhost:1433/MyDatabase?driver=SQL+Server+Native+Client+11.0?trusted_connection=no')

DBSession = sessionmaker(bind=engine)

session = DBSession()
db = Db(session)
print "the widget number is: "+db.widgetNumber

I faced the same issue and the problem was the database name.
I was putting the database name between brackets, like [DB_NAME], however as soon as I removed the brackets to DB_NAME it worked fine.
Please give it a try.

在obdc数据源中配置MSSQL服务器，并为pyodbc连接给予名称，如下所示。

import pyodbc

cnxn = pyodbc.connect('DSN=MyConnection')
cursor = cnxn.cursor()
cursor.execute("SELECT TOP (1000) [DepartmentID]      ,[Name]      ,[GroupName]      ,[ModifiedDate]  FROM ["
               "AdventureWorks2019].[HumanResources].[Department]")
rows = cursor.fetchall()
for row in rows:
    print(row.DepartmentID, row.Name)

这对我很有效。如果有其他方法可以做到这一点，请告诉我。

The important parameter is where the “username and password” were set, I am replacing it with “Trusted_Connection=yes” so the user account logged into Windows is used instead.

import pyodbc

conn_str = ("Driver={SQL Server};"
                           "Server=<server-name>;"
                            "Database=<db-name>;"
                            "Trusted_Connection=yes")

conn = pyodbc.connect(conn_str)

cursor = conn.cursor()