General exact solutions of the second-order homogeneous algebraic differential equations

摘要

The second-order homogeneous algebraic differential equation is studied, where are known such that is non-singular for some . A formula for the general exact solutions of the above equation is provided under the condition that there exists , such that . For a special second-order homogeneous algebraic differential equation coming from a physics model investigated by Bhat and Bernstein, a detailed description is given about how to construct a particular solution of the latter quadratic matrix equation.