If your Rasmus Hansen was the one born 9 March 1874, he was born in Skanderborg, not Odense:
Please read ALL the replies, as the one in Odense was a false alarm based on misinterpretation of the all-numeric date format you used.
Here you will see a map of the Danish Amts (Counties): http://www.dis-danmark.dk/kort/kort.htm
Click on Skanderborg and you will find Yding parish in the upper portion of Voer Herred (district).
Rasmus' father was born in Hornborg parish, lower part of Nim Herred, and his mother in Ry, west part of Hjelmslev district.