线性常微分方程的一点结论及其应用

Conclusion and Applications of Linear Ordinary Differential Equations

线性常微分方程解的理论具有广泛的应用性并已发展得十分成熟。本文给出由若干解确定出其满足的线性常微分方程表达式的公式,代数线性方程组理论与行列式理论在公式推导过程中起了关键作用。基于推导所得公式,对若干大学生数学竞赛题与考研数学题给出统一处理。

The solvability theory of linear ordinary differential equations has been widely applied and developed very well.A formula to determinine the expressions of linear ordinary differential equations satisfied by several solutions is given here.Theory of linear systems of algebraic equations and determinant theory play a key role in the derivation of the formula.Based on the new-obtained formula,several contest problems and NEEP mathematics problems are treated in a unified way.