本文系统介绍一般线性微分方程的部分解法，包括：变量变换法（欧拉方程、降阶法、特殊变系数方程）、变动任意常数法、幂级数解法（定理、\gamma 阶贝塞尔方程及其解）。

本文将系统介绍常系数线性微分方程的解法方法，分别包括二阶常系数齐次线性微分方程、n 阶常系数齐次线性微分方程、以及常系数非齐次线性微分方程的解法。详细推导各步骤，便于理解和掌握。

The bars is subjected to a pair of longitudinal forces with equal magnitude and opposite directions, and the line of action forces coincides with the axis of the bar.

The internal force of a member is not uniformly distributed in most cases, so the definition of internal force concentration is not only accurate but also important, because failure or damage often starts from the place where the internal force concentration is the greatest. The definition of internal force concentration is called stress. Stress is the internal forces per unit area, or the intensity of internal force distributed over a given section.

实际的电路元件，例如电感，，除了电感本身的功能，实际上存在寄生电容和寄生电阻，通常做理想处理，只关注其电感。

Mechanics of materials mainly studies the deformation of deformable body under external forces,, the additional internal forces caused by the deformation, the failure caused by the internal forces, and the criteria to avoid/control the failure. Moreover, on the basis of above, derives the basic method of static design of engineering members or components.

由数学方法解决实际问题时，通常按照以下过程：

函数f(x)是变量x的函数，且u(x)=\frac{\mathrm{d}}{\mathrm{d}x}f(x)，可以构造一个新的以u为自变量的函数：

一般地，质点系各个质点的矢量坐标可以表示为广义坐标的函数\vec{r}=\vec{r}_i(q_1,q_2,\cdots,q_k;t)。质点速度相应地通过广义速度表示为：

前面已经求出\nu阶贝塞尔方程的通解，即：

一般情况下，一个由n质点组成的质点系在空间的位形用直角坐标来确定需要3n个坐标，即：

格林函数又称点源函数，代表一个点源在一定的边界条件和（或）初始条件下所产生的场，知道了点源的场就可以用叠加的方法求出任意源所产生的场。冲量定理是在时间域上进行叠加，这里把问题扩充到空间域上进行叠加。形式为：