摘要
从几何实例引入了一类新的常微分方程 ,运用初等代数的方法证明了这类微分方程是具有初等解析解的 ,并引入了特征方程的概念 ,给出了通解的代数表达式 。
A kind of new ordinary differential equation was first obtained from a geometic example,then it was proved to have elementary analytic solution with the method of elementary algebraic.The concept of characteristic equation was also introduced and the algebraic expression formula of its general solution was given,thus the closed sovable range of ordinary differential equation was extended.
关键词
常微分方程
可解类型
特征方程
初等解析解
通解
特征根
ordinary differential equation
new solvable types
characteristic equation
elementary anlytic solution
