Separation of variables: Difference between revisions
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(Created page with "'''Separation of variables''' is a technique to solve differential equations. It requires the equation to be ''separable''; that is, the equation is of the form <math> y' = F(y) G(t) </math> where the RHS is the product of a function of y and a function of t. = Procedure = Divide both sides by <math>F(y)</math>, integrate, and you get an Implicit equation of y in terms of t. Category:Differential Equations") |
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where the RHS is the product of a function of y and a function of t. | where the RHS is the product of a function of y and a function of t. | ||
It is considered to be easier than [[Integrating factor]] when both options are available. | |||
= Cases = | |||
Two notable cases are [[homogeneous]] [[Linear First Order ODE|linear first order ODE]]<nowiki/>s and [[Autonomous ODE]]<nowiki/>s. | |||
= Procedure = | = Procedure = | ||
Latest revision as of 23:38, 23 April 2024
Separation of variables is a technique to solve differential equations. It requires the equation to be separable; that is, the equation is of the form
where the RHS is the product of a function of y and a function of t.
It is considered to be easier than Integrating factor when both options are available.
Cases
Two notable cases are homogeneous linear first order ODEs and Autonomous ODEs.
Procedure
Divide both sides by , integrate, and you get an Implicit equation of y in terms of t.
