Do the gospels disagree on where Jesus was born?

The two gospel writers Matthew and Luke agree that Jesus was born in Bethlehem. Mark and John do not cover the birth of Jesus.

Matthew 2:1 Now after Jesus was born in Bethlehem of Judea in the days of Herod the king, behold, wise men from the east came to Jerusalem,

Luke 2:4-7 4 And Joseph also went up from Galilee, from the town of Nazareth, to Judea, to the city of David, which is called Bethlehem, because he was of the house and lineage of David, 5 to be registered with Mary, his betrothed, who was with child. 6 And while they were there, the time came for her to give birth. 7 And she gave birth to her firstborn son and wrapped him in swaddling cloths and laid him in a manger, because there was no place for them in the inn.

No disagreements or contradictions.

_{Image courtesy of Geralt}