Separable differential equation
Encyclopedia
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
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Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, a separable differential equation
Differential equation
A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders...
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
Separation of variables
In mathematics, separation of variables is any of several methods for solving ordinary and partial differential equations, in which algebra allows one to rewrite an equation so that each of two variables occurs on a different side of the equation....
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- For ordinary differential equationOrdinary differential equationIn mathematics, an ordinary differential equation is a relation that contains functions of only one independent variable, and one or more of their derivatives with respect to that variable....
s, it describes a class of equations that can be separated into a pair of integralIntegralIntegration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus...
s. See examples of differential equationsExamples of differential equationsDifferential equations arise in many problems in physics, engineering, and other sciences. The following examples show how to solve differential equations in a few simple cases when an exact solution exists....
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- For partial differential equationPartial differential equationIn mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...
s, it describes a class of equations that can be broken down into differential equations in fewer independent variables. See separable partial differential equationSeparable partial differential equationA separable partial differential equation is one that can be broken into a set of separate equations of lower dimensionality by a method of separation of variables. This generally relies upon the problem having some special form or symmetry...
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