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一类常系数非齐次线性微分方程特解的矩阵表示

Matrix Representation for a Particular Solution to a Class of Inhomogeneous Linear Differential Equation with Constant Coefficients

  • 摘要: 运用微分逆算子移位定理和矩阵运算将一类一阶常系数非齐次线性微分方程的特解用矩阵的形式表示,并在此基础上利用欧拉公式将另一类一阶常系数非齐次线性微分方程的特解也用矩阵的形式表示,用此方法不仅可以简便快捷地计算出这些微分方程的特解,且容易掌握,还可推广到求高阶常系数非齐次线性微分方程的特解.

     

    Abstract: In the report, the differential inverse operator shift theorem and matrix operation were used to show the particular solution for a class of 1st-order inhomogeneous linear differential equation with constant coefficients in the form of matrix, and on which Euler’s formula was used to show the particular solution for another class of 1st-order inhomogeneous linear differential equation with constant coefficients in the form of matrix. The method, which is easy to master, not only work out the particular solution to such differential equations very easily, but also can be applied to seeking a particular solution to a higher-order homogeneous linear differential equation with constant coefficients.

     

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