Abstract
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.
Acknowledgements
The authors thank Professor Nung-Sing Sze for his help. They also thank the referee for many detailed suggestions and helpful comments, which have improved this paper significantly.
Notes
1 Note that by (Equation4545 ) any solution of is nonzero.
Supported by the National Natural Science Foundation of China [grant number 11171222] and the Innovation Program of Shanghai Municipal Education Commission [grant number 12ZZ129].