Based on the provided text, analyze the psychological journey of the doctor's family from despair to hope through their encounter with Sai Baba.

Chapter 34 of the Shri Sai Satcharitra masterfully charts the family's emotional trajectory from utter despair to renewed hope. Initially, they were mired in helplessness as all medical interventions, including those by expert surgeons, failed to cure the boy's painful bone-cyst. The text notes they were "exhausted and felt helpless," and seeing their son's suffering left them "greatly exhausted." This despair led them to try worshipping deities, but with no success. The turning point came when they heard of Sai Baba. Their decision to go to Shirdi was described as a "last resort," indicating their desperation. Upon meeting Sai, they pleaded with "choked voice" and "pitiful faces." The climax of their journey is Sai Baba's compassionate response. He, the "embodiment of compassion," reassures them, telling them to "remain worry-free" and that those who seek shelter in his Masjid shall never face downfall. This divine assurance, coupled with the tangible gift of Udi, transformed their desperation into firm hope for their child's recovery.