Love Hina Spring Movie(2001)

Love Hina: Haru Special - Kimi Sakura Chiru Nakare!!

The tests have come, and Keitaro can only hope to succeed. However, in the final stretch, he fails miserably and daydreams through the test. Assuming that he has failed, he runs away, so the rest of the cast hunts him down on a remote desert island to bring him back.
The Toudai entrance exams have finally come (again) for Keitaro. With all his confidence Keitaro sits for the paper, but ends up falling asleep and dreaming about Narusegawa. Waking up with barely any time to complete the paper, Keitaro thinks he will fail the paper and tries to escape from Hinata Lodge and forget all the memories with it. By a stroke of luck he meets Seta, but ends up in a faraway island with the whole cast trying to look for him.

(Source: Anime News Network)