一类变系数三阶线性微分方程求解及Maple实现

Solving and Implementing by Maple for a Class of Three-Order Linear Differential Equations With Variable Coefficients

三阶线性微分方程的求解问题是常微分方程课程中的一类重要问题。然而,变系数微分方程往往比常系数微分方程的求解要复杂很多。文章通过判断变系数三阶线性微分方程常系数化的条件,运用Maple软件把变系数三阶线性微分方程转化为常系数三阶线性微分方程。结合变系数三阶微分方程的Maple直接求法,得出的常系数化后的结果更精确。

Solving the three- order linear differential equations is an important problem in the class ofordinarydifferentialequation. However,thecase becomes more intricate for variable- coefficient differential equations than the ones with constant- coefficient. By judging the conditions from the variable- coefficient case to the constant- coefficient case and combing with the function of transforming from the variable- coefficient case to constant- coefficient one for the software of Maple,it is much more accurate for the results of constant- coefficient differential equations than before.