The Explicit Solution of Homogeneous Linear Ordinary Differential Equations with Constant Coefficients

Huang Yong-nian

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1992 > 13(12): 1069-1074

Huang Yong-nian. The Explicit Solution of Homogeneous Linear Ordinary Differential Equations with Constant Coefficients[J]. Applied Mathematics and Mechanics, 1992, 13(12): 1069-1074.

Citation:

Huang Yong-nian. The Explicit Solution of Homogeneous Linear Ordinary Differential Equations with Constant Coefficients[J]. Applied Mathematics and Mechanics, 1992, 13(12): 1069-1074.

Citation:

Huang Yong-nian. The Explicit Solution of Homogeneous Linear Ordinary Differential Equations with Constant Coefficients[J]. Applied Mathematics and Mechanics, 1992, 13(12): 1069-1074.

PDF( 335 KB)

The Explicit Solution of Homogeneous Linear Ordinary Differential Equations with Constant Coefficients

Huang Yong-nian

Department of Mechanics, Peking University, Beijing

Received Date: 1991-10-25
Publish Date: 1992-12-15

Abstract

Abstract

In this paper by using tensor analysis we give the explicit expressions of the solution of the initial-value problem of homogeneous linear differential equations with constant coefficients and the nth-order homogeneous linear differential equation with constant coefficients.In fact,we give the general formula for calculating the elements of the matrix e^At.We also give the results when the characteristic equation has the repeated roots.The present method is simpler and better than the other methods.
- tensor differential equation,
- characteristic tensor,
- explicit solution

FullText(HTML)

References(2)

References

[1]	王柔怀、伍卓珊,《常微分方程讲义》,人民教育出版社(1963).146.
[2]	王高维、周之铭等,《常微分方程》(第2版),高等教育出版社(1983),223.