CALCULUS Understanding Its Concepts and Methods

Separation of variables

Separation of variables is a technique to solve first-order ordinary differential equations. You rearrange the equation, if you can, so that all terms involving one of the variables are on one side of the equation, and all terms involving the other variable are on the other side. Integrating both sides completes the solution. You can't always separate the variables. Even when you can, you may not be able to perform the two integrations.

Example. Given a differential equation in the formyou can divide by to getso

This
separates the variables:
*y*
(and
*dy*
on the left and
*x*
(and
*dx*)
on the right.

If we can do the integrations, then
will
give us a relationship between
*y*
and
*x*.

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Separable differential equation

Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.