Using the Routh-Hurwitz criterion presented in Nelson's book, we can determine that the aircraft is dynamically stable if the stability derivative matrix has a positive determinant.
Flight Stability and Automatic Control by Robert C. Nelson is a cornerstone textbook for aerospace engineering students. It bridges the gap between basic aerodynamics and complex flight dynamics. However, the mathematical rigor required to solve its problems often leads students to search for the official solutions manual to verify their work and master the material. Flight Stability And Automatic Control Nelson Solutions