How did harry solve his problem in the prissiner of askiban?

In "Harry Potter and the Prisoner of Azkaban," Harry solves his problem of saving Sirius Black and himself from the Dementors by using a powerful spell called the Patronus Charm. With the help of Professor Lupin, he learns to conjure a Patronus, which takes the form of a stag. During the climax, Harry realizes he must produce the Patronus to save both himself and his future self, ultimately succeeding in protecting Sirius from the Dementors. This act not only showcases Harry's growth but also highlights the importance of believing in oneself.