# Separable differential equation

Separable differential equation

In mathematics, a separable differential equation may refer to one of two related things, both of which are differential equations that can be attacked by a method of separation of variables.

* For ordinary differential equations, it describes a class of equations that can be separated into a pair of integrals. See: Examples of differential equations

* For partial differential equations, it describes a class of equations that can be broken down into differential equations in fewer independent variables. See Separable partial differential equation.

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• Separable partial differential equation — A separable partial differential equation (PDE) is one that can be broken into a set of separate equations of lower dimensionality (fewer independent variables) by a method of separation of variables. This generally relies upon the problem having …   Wikipedia

• Partial differential equation — A visualisation of a solution to the heat equation on a two dimensional plane In mathematics, partial differential equations (PDE) are a type of differential equation, i.e., a relation involving an unknown function (or functions) of several… …   Wikipedia

• Homogeneous differential equation — A homogeneous differential equation has several distinct meanings.One meaning is that a first order ordinary differential equation is homogeneous if it has the form : frac{dy}{dx} = F(y/x).To solve such equations, one makes the change of… …   Wikipedia

• separable — separability, separableness, n. separably, adv. /sep euhr euh beuhl, sep reuh /, adj. 1. capable of being separated, parted, or dissociated. 2. Math. a. containing a countable dense subset. b. (of a differential equation) capable of being written …   Universalium

• List of solution strategies for differential equations — Exact= * Method of undetermined coefficients * Integrating factor:For y +a(x)y = b(x) let M(x)=exp{int a(x),dx} then::y(x) = frac{int b(x) M(x), dx + C}{M(x)}., * Method of variation of parameters * Separable differential equationNumerical… …   Wikipedia

• Examples of differential equations — Differential equations arise in many problems in physics, engineering, etc. The following examples show how to solve differential equations in a few simple cases when an exact solution exists. eparable first order linear ordinary differential… …   Wikipedia

• Hamilton–Jacobi equation — In physics, the Hamilton–Jacobi equation (HJE) is a reformulation of classical mechanics and, thus, equivalent to other formulations such as Newton s laws of motion, Lagrangian mechanics and Hamiltonian mechanics. The Hamilton–Jacobi equation is… …   Wikipedia

• Electromagnetic wave equation — The electromagnetic wave equation is a second order partial differential equation that describes the propagation of electromagnetic waves through a medium or in a vacuum. The homogeneous form of the equation, written in terms of either the… …   Wikipedia

• Helmholtz equation — The Helmholtz equation, named for Hermann von Helmholtz, is the elliptic partial differential equation:( abla^2 + k^2) A = 0where abla^2 is the Laplacian, k is a constant, and the unknown function A=A(x, y, z) is defined on n dimensional… …   Wikipedia

• Schrödinger equation — For a more general introduction to the topic, please see Introduction to quantum mechanics. Quantum mechanics …   Wikipedia