Second Order Non-homogeneous Differential Equation
二阶非齐次微分方程
Many physical problems involve second order differential equations. Some applications involve homogeneous equations, but the more general case is the non-homogeneous equation. The general form of the second order differential equation is
The path to a general solution involves finding a solution fh(x) to the homogeneous equation, and then finding a particular solution fp(x) to the non-homogeneous equation (i.e., find any solution that satisfies the equation with all terms included). The form of the general solution is
通向一般解的路径涉及求解齐次方程的解 f_h(x)，然后求解非齐次方程的特解 f_p(x)（即找到任何满足包含所有项的方程的解）。一般解的形式为
许多物理问题涉及二阶微分方程。一些应用涉及齐次方程，但更一般的情况是非齐次方程。二阶微分方程的一般形式是
A great variety of types of solutions arise in physical problems and specific functions arise, depending upon the boundary conditions.
| Example of mass on spring
弹簧上的质量示例 |
在物理问题中，会涌现出各种各样的解，具体函数的类型则取决于边界条件。
References
Kreyzig
Ch 2
索引参考 Kreyzig 第2章
| HyperPhysics****HyperMath*****Differential equations
HyperPhysics **** HyperMath ***** 微分方程 | R Nave |
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