What would you say inspired the writing of the Aeneid and the Odyssey. Something that is relevant to both poems.

Iliad and Odyssey were composed and recited long before they were ever written down. They arose in the areas around ancient Greece and were told and retold for several hundred years before they were written down.

http://en.wikipedia.org/wiki/Iliad
There are still disagreements about who actually composed these or even it they were composed by a single person.

Aeneid, however, was written purposefully by the Roman poet Vergil (sometimes spelled Virgil). His inspiration was a character already known in the Roman world from Greek mythology (Aeneus), but Vergil wrote this poem to give people a strong connection between the young Roman culture and the ancient Greeks.
http://en.wikipedia.org/wiki/Aeneid

I always told my classes that writers motive has always been from earliest times - Does man or god control man's fate? Look for this theme in both of these stories. You might also check these sites.

http://www.sparknotes.com/lit/aeneid/themes.html

http://www.sparknotes.com/lit/odyssey/themes.html

Both the Aeneid and the Odyssey were epic poems that have greatly impacted Western literature. While they are two separate works, they do share a common inspiration — the rich mythology and oral tradition of ancient Greece.

To understand the inspiration behind both poems, let's start with the Odyssey. Composed by the Greek poet Homer, the Odyssey tells the story of Odysseus' long journey back home after the Trojan War. It draws upon a vast body of myths and legends that were part of the oral tradition in ancient Greece. These myths were passed down through generations, told and retold by bards and poets, before being written down.

Similarly, the Aeneid, written by the Roman poet Virgil, is heavily influenced by Greek mythology. It follows the hero Aeneas as he embarks on a perilous journey, fleeing the fallen city of Troy to establish a new home in Italy. Virgil borrowed from various Greek myths, incorporating them into the narrative to connect Rome's origin story to the glorious tales of the Greek heroes.

So, to pinpoint the common inspiration behind both the Aeneid and the Odyssey, we can say it lies in the rich and diverse mythology of ancient Greece. By drawing from these myths, both Homer and Virgil sought to create captivating narratives that entertained, taught moral lessons, and celebrated the heroic ideals of their respective cultures.