Separation of variables

Summary

Separation of variables is a method for solving differential equations by splitting the dependence on different variables. For an ordinary differential equation $y' = g(x)\, h(y)$, one moves the $y$ terms to one side and the $x$ terms to the other and integrates. Such equations are called separable equations. For a linear partial differential equation, one looks for solutions that are products of functions of one variable each. This turns the equation into several ordinary differential equations. It is one of the oldest and most used solution methods. See the definition.