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第157行：
第157行： − + − + 第167行：
第167行： − 线性微分方程是在未知函数及其导数中线性的微分方程。他们的理论发展得很好，在许多情况下可以用积分来表示他们的解。+ 第175行：
第175行： − + 第183行：
第183行： − 一般来说，微分方程的解不能用解析解表示，数值方法通常用于在计算机上求解微分方程。+
→Ordinary differential equations
An [[ordinary differential equation]] (''ODE'') is an equation containing an unknown [[function of a real variable|function of one real or complex variable]] {{mvar|x}}, its derivatives, and some given functions of {{mvar|x}}. The unknown function is generally represented by a [[variable (mathematics)|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 a real variable|function of one real or complex variable]] {{mvar|x}}, its derivatives, and some given functions of {{mvar|x}}. The unknown function is generally represented by a [[variable (mathematics)|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 ), which, therefore, depends on . Thus 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.
常微分方程中，包含有：只含有一个实变量或复变量的未知函数及其导数以及一些已知的函数。未知函数通常由一个变量(通常表示)表示，因此这个变量依赖于。因此通常被称为方程式的自变量。“普通”一词与偏微分方程一词形成对比，后者可能涉及一个以上的独立变量。
常微分方程中，包含有：只含有一个实变量或复变量的未知函数及其导数以及一些已知的函数。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形成对比，后者可能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.
线性微分方程是关于指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。
Most ODEs that are encountered in physics are linear. Therefore, most special functions may be defined as solutions of linear differential equations (see Holonomic function).
Most ODEs that are encountered in physics are linear. Therefore, most special functions may be defined as solutions of linear differential equations (see Holonomic function).
物理学中遇到的大多数常微分方程都是线性的。因此，大多数特殊函数可以定义为线性微分方程的解(见完整函数)。
物理学中遇到的大多数常微分方程都是线性的。因此，大多数特殊函数可以定义为线性微分方程的解(见完整性函数)。
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.
一般来说，微分方程的解不能用解析解表示，通常会在计算机上利用数值方法求解微分方程。
===Partial differential equations===
===Partial differential equations===