常微分方程理论中的一个经典问题

A classic problem in the theory of ODEs

实解析微分方程x=f（t,x）的解不一定实解析.实多项式微分方程x=p（t,x）的解一定实解析.文章修正了在复微分方程到微分方程的推理中引起的一个误解.

A solution of the real analytic differential equation x=f(t, x) may not be analytic. Any solution of the real algebraic differential equation x= p(t, x) must be analytic. This paper indicates a misunderstanding on the restriction of a complex differential equation to a real differential equation.