线性微分方程组dY/dx=A(x)Y的基本解组新探

A New Research on Solution of Linearity Differential Equations dY/dx=A(x)Y

对变系数线性齐次微分方程组的特殊类型的求解问题进行了探讨,给出了系数矩阵为A(x)(各元素为x的多项式)的一阶线性齐次微分方程组解的结构定理,以及系数矩阵为Af(x)(A为n阶常数矩阵,f(x)为可积函数)的一阶线性齐次微分方程组解的结构定理,并通过实例给出了具体的求解方法。

Investigates the solution of special variable coefficient linearity homogeneous differential equations. Presents the structure theorem of first-order linear homogeneous differential equations with coefficient matrix A（x）（each element is polynomial of x） and the structure theorem with coefficient matrix Af（x） （A is n th ordinary matrix andf（x） is an integral function）. And provides specific solving methods through examples.