本文应用可积的一类线性微分方程求出了非均质变截面弹性直杆振动问题的一个精确解，我们应用这一精确解验证了渐近解的精确度。
This paper gives an exact solution for free vibration of a physically nonuniform straight bar with varying section by the use of a class of integrable linear ordinary differential equation.
对于二阶变系数线性微分方程来说，这也是可积的一个充分条件。
It is also a sufficient condition for second order linear differential equation with varied coefficient to be integrable.
对二阶变系数非线性微分方程的常系数化给出两个使其可积的条件，并举例论证。
The two conditions of the second order nonlinear differential equation with variable coefficient are given and expounded with examples.
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