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第147行：
第147行： − 微分方程可分为几种类型。除了描述方程本身的性质之外，微分方程的类型有助于指导选择何种解决方案。常见的区别包括方程是否为: 常微分/偏微分方程、线性/非线性方程和齐次/非齐次方程。这份清单还很长，微分方程还有许多在特定的情况下非常有用的其他性质和子类。+ 第160行：
第160行： − 常微分方程是只含有一个实变量或复变量的未知函数，其导数以及此函数的一些方程。未知函数通常由一个变量(通常由 {{mvar|y}} 表示)表示，因此这个变量依赖于 {{mvar|x}} 。因此 {{mvar|x}} 通常被称为方程式的自变量。“常微分方程”一词与偏微分方程一词相比，后者涉及一个以上的独立变量。+ 第168行：
第168行： − 线性微分方程是指方程中未知函数及其导数都是线性的微分方程。关于这些方程的理论发展得很好，在多数情况下可以用积分来表示他们的解。+ 第184行：
第184行： − 一般来说，微分方程的解不能用解析解表示，而通常会在计算机上利用数值方法求解微分方程。+ 第195行：
第195行： − + 第203行：
第203行： − 偏微分方程可以用来描述自然界中各种各样的现象，如声音、热量、静电、电动力学、流体流动、弹性或量子力学。这些看起来截然不同的物理现象可以用相似的偏微分方程表达。正如常微分方程经常对一维动力系统进行建模一样，偏微分方程经常对多维系统进行建模。随机偏微分方程延伸了偏微分方程在模拟随机性上的应用。+
→Types
Differential equations can be divided into several types. Apart from describing the properties of the equation itself, these classes of differential equations can help inform the choice of approach to a solution. Commonly used distinctions include whether the equation is: Ordinary/Partial, Linear/Non-linear, and Homogeneous/heterogeneous. This list is far from exhaustive; there are many other properties and subclasses of differential equations which can be very useful in specific contexts.
Differential equations can be divided into several types. Apart from describing the properties of the equation itself, these classes of differential equations can help inform the choice of approach to a solution. Commonly used distinctions include whether the equation is: Ordinary/Partial, Linear/Non-linear, and Homogeneous/heterogeneous. This list is far from exhaustive; there are many other properties and subclasses of differential equations which can be very useful in specific contexts.
微分方程可分为以下几种类型。除了描述方程本身的性质之外，微分方程的多种类型为我们选择何种解决方案提供了多种指导。常见的微分方程有: 常微分/偏微分方程、线性/非线性方程和齐次/非齐次方程。微分方程还有许多类型，以及许多在特定的情况下实用的其它性质和子类。
An ordinary differential equation (ODE) is an equation containing an unknown function of one real or complex variable , its derivatives, and some given functions of . The unknown function is generally represented by a variable (often denoted {{mvar|y}}), which, therefore, depends on {{mvar|x}}. Thus {{mvar|x}} is often called the independent variable of the equation. The term "ordinary" is used in contrast with the term partial differential equation, which may be with respect to more than one independent variable.
An ordinary differential equation (ODE) is an equation containing an unknown function of one real or complex variable , its derivatives, and some given functions of . The unknown function is generally represented by a variable (often denoted {{mvar|y}}), which, therefore, depends on {{mvar|x}}. Thus {{mvar|x}} is often called the independent variable of the equation. The term "ordinary" is used in contrast with the term partial differential equation, which may be with respect to more than one independent variable.
常微分方程是只含有一个实变量或复变量的未知函数，其导数以及此函数的一些方程。未知函数因变量(通常由 {{mvar|y}} 表示)，其常常随 {{mvar|x}}的变化而变化 。因此 {{mvar|x}} 通常被称为方程式的自变量。“常微分方程”一词与偏微分方程一词相比，后者涉及一个以上的独立变量。
Linear differential equations are the differential equations that are linear in the unknown function and its derivatives. Their theory is well developed, and in many cases one may express their solutions in terms of integrals.
Linear differential equations are the differential equations that are linear in the unknown function and its derivatives. Their theory is well developed, and in many cases one may express their solutions in terms of integrals.
线性微分方程是指方程中未知函数及其导数都是线性的微分方程。关于这些方程的理论发展得很好，在多数情况下可以用积分来表示它们的解。
As, in general, the solutions of a differential equation cannot be expressed by a closed-form expression, numerical methods are commonly used for solving differential equations on a computer.
As, in general, the solutions of a differential equation cannot be expressed by a closed-form expression, numerical methods are commonly used for solving differential equations on a computer.
一般地，微分方程的解不能用解析解表示，而会在计算机上利用数值方法求解。
===Partial differential equations===
===Partial differential equations===
A partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. (This is in contrast to ordinary differential equations, which deal with functions of a single variable and their derivatives.) PDEs are used to formulate problems involving functions of several variables, and are either solved in closed form, or used to create a relevant computer model.
A partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. (This is in contrast to ordinary differential equations, which deal with functions of a single variable and their derivatives.) PDEs are used to formulate problems involving functions of several variables, and are either solved in closed form, or used to create a relevant computer model.
'''<font color="#ff8000">偏微分方程 Partial Differential Equation</font><font>'''是一种包含多元函数及其偏导数的微分方程函数(这与处理单变量函数及其导数的常微分方程不同)。偏微分方程用于描述涉及多元函数的问题，或者以封闭形式求解，或者用于创建相关的计算机模型。
'''<font color="#ff8000">偏微分方程 Partial Differential Equation</font><font>'''是一种包含多元函数及其偏导数的微分方程函数(这与处理单变量函数及其导数的常微分方程不同)。偏微分方程可用于描述涉及多元函数的问题求闭式解，或者用于创建相关的计算机模型。
PDEs can be used to describe a wide variety of phenomena in nature such as sound, heat, electrostatics, electrodynamics, fluid flow, elasticity, or quantum mechanics. These seemingly distinct physical phenomena can be formalized similarly in terms of PDEs. Just as ordinary differential equations often model one-dimensional dynamical systems, partial differential equations often model multidimensional systems. Stochastic partial differential equations generalize partial differential equations for modeling randomness.
PDEs can be used to describe a wide variety of phenomena in nature such as sound, heat, electrostatics, electrodynamics, fluid flow, elasticity, or quantum mechanics. These seemingly distinct physical phenomena can be formalized similarly in terms of PDEs. Just as ordinary differential equations often model one-dimensional dynamical systems, partial differential equations often model multidimensional systems. Stochastic partial differential equations generalize partial differential equations for modeling randomness.
偏微分方程可以用来描述自然界中各种各样的现象，如声音、热量、静电、电动力学、流体流动、弹性和量子力学等。这些看起来截然不同的物理现象其实都可以用相似的偏微分方程表达。正如常微分方程常被用于对一维动力系统进行建模一样，偏微分方程常被用于对多维系统进行建模。随机偏微分方程延伸了偏微分方程在模拟随机性上的应用。
===Non-linear differential equations===
===Non-linear differential equations===