General solutions to the a-class systems of second-order ordinary differential equation

By reducing order and using Euler's eigenvalue method,the general solution formula to a kind of three-dimensional second-order ordinary differential equation groups with constant coefficients is obtained.The methods used to solve the problems in this paper are compared with that 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.