Oedipus is trying to find the murderer of the former king Laius in order to avenge his death and bring justice to the kingdom. Oedipus feels that it is his duty as king to seek justice for the murdered king, who was highly respected by all of Thebes.
Oedipus is also trying to find the murderer in order to prevent further chaos and bloodshed in the kingdom, as Laius was a much-loved and respected ruler. If Oedipus does not act quickly, there will be further unrest among the people of Thebes who are already grieving their lost king.
He is aware that the murderer is still at large and is likely to strike again, so he feels it is his responsibility to find and stop him. If Oedipus did not try to catch the murderer, then another person could be killed by him or her and there would be even more chaos in Thebes.
Oedipus is driven by his own personal sense of justice and morality, and feels that it is his responsibility to find the killer. He does not want anyone else’s life on his conscience if he can prevent it from happening through his actions or inaction.
As soon as Oedipus learns that the killer is still at large, he becomes determined to find him. He wants to bring peace and stability back to Thebes by finding and punishing the man who murdered Laius.
Oedipus has good reasons for trying to find the murderer; not only does he want to protect his city from further violence but also he feels a sense of responsibility towards the people of Thebes. He knows that they are depending on him to resolve this situation, so he feels compelled to use all of his resources in order to achieve justice.
Oedipus’ sense of responsibility is also evident in his willingness to sacrifice everything in order to achieve justice. He is prepared to risk his own life in order to find Laius’ killer.