Hello Kenya, They are totally the same. However, in conversation we say いく, some stories have ゆく, so in my opinion, いく is used in conversation, ゆく is used in writing, but not all the time.

It's a kind of collocation, e.g. a train bound for somewhere is ～行き（ゆき）not いき.

Differences in pronunciation

One thing to keep in mind is that the -te form of 行く is いって (itte). You cannot say ゆって (yutte).