Oxford Calculus: Separation of Variables Integration Technique Explained with Examples

University of Oxford mathematician Dr Tom Crawford explains how to use the method of separation of variables to solve first order separable differential equations. Test yourself with some exercises on the separation of variables technique for solving differential equations with this FREE worksheet in Maple Learn here.

The separation of variables technique is introduced for a general first order separable differential equation, and then used to solve two problems with fully worked example solutions. The first example requires manipulation of a fraction, and the second a substitution and the use of some trigonometric identities. In both cases the solution is checked by calculating derivatives, with the second one requiring implicit differentiation due to the solution being given implicitly.