A note on the solution of third order matrix differential equations
LIU Zhihui
LIAO Meiting
LIANG Hongxue
Abstract：This paper discusses the third-order differential equations without first order items.According to the theory of higher order equations and the theory of Matrix,this paper first reduces the lower order of homogeneous equations by the method of degradation.Then,using Cardan formula and Euler method,the general solution of the homogeneous expression of a class of two dimensional,third order constant coefficient differential equation is obtained.Furthermore,one special solution formula of trigonometric function multiplying exponential function is studied by using the method of undetermined Matrix and comparing by column,the accuracy of the general solution and the special solution of the equation is verified by an example.
Keywords：differential equationscharacteristic root methodundetermined matrix methodgeneral solution formulaparticular solution formula
Publication Date：2025-11-30
Online Publishing Date：2025-12-12(First online date of this platform, not the publication date of the document)
Pages：5( 56-60 )