A Method to Get the General Solutions of Linear Differential Equation or Equations with Constant Coefficients Based on Laplace Transformation

Abstract

In management science research, a large number of cases analysis often requier from qualitative analysis to quantitative analysis, differential equation and differential equations are often used in quantitative analysis. The core of quantitative analysis of a case is to build a corresponding mathematical model. The differential equation models are widely used mathematical models. In particular, linear differential equation models with constant coefficients are often used mathematical models in the quantitative analysis of cases in management science research. In practice, the particular solution of linear differential equation model with constant coefficients often been found by Laplace transformation. Follow this way, a method to get the general solutions of linear differential equation with constant coefficients based on Laplace transformation be given. In this method, it is easy to find the general solution of homogeneous linear differential equation, of non-homogeneous linear differential equation and of linear differential equations with constant coefficients based on Laplace transformation.

Key words: Management; Mathematical model; Linear differential equation; Laplace transformation