Odysseus is an example of a dynamic character because

he is gone from home for years and misses his family.
he experiences success in battle and is assisted by the gods.
he has been a beloved literary hero for hundreds of years.
he changes in important ways over the course of his journey.

The correct answer is the last option. Odysseus is an example of a dynamic character because he changes in important ways over the course of his journey. In literature, a dynamic character is one which shows markable character development and that changes over the course of their journey, rather than simply remaining a two dimensional character that acts as little more than an agent of the author.