In daily conversations, 行く　いく　is used more frequently. However, ゆく is found more in poetic scripts as well as formal scripts.

Hola First of all, please wait for the answers of people who know about the Japanese more than me. According to the dictionary and some web pages, both are correct and now ゆく is for written language and いく is more colloquial. However, some words should be read ゆく, for example, ゆく年[とし]、ゆく末[すえ]、行方[ゆくえ]、過ぎゆく、消えゆく、etc...and it better to memorize them as a word/expressions. Besides, there are differences between their conjugations. We have ゆかない、ゆきます、ゆく、ゆけば、ゆこう, with か、き、く、け、こ. However, now ゆく doesn't conjugate ゆって、ゆった、ゆったり but we have いって、いった、いったり for いく. Espero que te ayude. Y espera mejor respuestas, por favor. Un saludo.