In the case of In re Application of Burwell (1955), a U.S. Supreme Court case, the court was asked to consider whether or not an individual could be compelled to answer questions before a grand jury when they believed that their answers may incriminate them. The petitioner, Burwell, had been subpoenaed by a federal grand jury and refused to answer certain questions on the grounds that his responses might tend to incriminate him. He was then held in contempt for refusing to testify and appealed this decision up through the courts until it reached the Supreme Court. The key issue at stake here was how far Fifth Amendment protections against self-incrimination extended in such circumstances. Ultimately, after considering previous precedents and interpretations of constitutional law, as well as arguments from both sides about potential implications for future cases if different rulings were made, the Supreme Court decided in favor of Burwell's right not to provide potentially self-incriminating testimony before a grand jury under these specific conditions.

The dissenting opinion in the case of In re Application of Burwell, 1955 is not readily available. This could be due to several reasons including that it may not have been a Supreme Court case or there might be some confusion with the name or year of the case. It's also possible that all justices agreed on the decision and thus, no dissenting opinion was written. Without specific details about this particular court proceeding, providing an accurate summary becomes challenging. Please verify these details for further assistance.