Go to the Samegawa Flood Plain and talk to the dog there. On a different day, speak with the dog at the north end of the Shopping District and "Talk to it gently." The next day, return to the Flood Plain and "Talk to it gently" there. Another day, the dog should be on the riverbank path. Give it a Steak Skewer from the Sonzai Daigaku to complete the sidequest.