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separation of variables
(redirected from Separation of variable)

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separation of variables [‚sep·ə′rā·shən əv ′ver·ē·ə·bəlz]
(mathematics)
A technique where certain differential equations are rewritten in the form ƒ(x)dx=g(y)dywhich is then solvable by integrating both sides of the equation.
A method of solving partial differential equations in which the solution is written in the form of a product of functions, each of which depends on only one of the independent variables; the equation is then arranged so that each of the terms involves only one of the variables and its corresponding function, and each of these terms is then set equal to a constant, resulting in ordinary differential equations. Also known as product-solution method.


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Formation of ordinary differential equations, solution of homogeneous differential equations, separation of variables method, linear first order differential equations.
95 Paperback Quantitative applications in the social sciences, a Sage pulications series; 7-150 QA371 Brown (Emory University) explains the separation of variables technique and three numerical methods for solving linear first-order differential equations as well as graphical techniques for analyzing systems of differential equations.
z=0] = 0 the method of separation of variables yields [P.
 
 
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