General Solutions to One Kind of Systems of Second-order Ordinary Differential Equation

By reducing order and using Euler's eigenvalue method,the general solution formula to one kind of three-dimensional second-order ordinary differential equation groups with constant coefficients is obtained.The methods used in this paper are compared with the method using Laplacian transform with examples.It is illustrated that using general solution formula to solve the high-order differential equation groups is more concise than other methods in accuracy,clarity and practicability.