Separable Equations

A separable differential equation is a first order differential equation that can be written in the form

$\displaystyle \frac{dy}{dx} = \frac{f(x)}{h(y)}.

These can be solved by integration, by noting that

$\displaystyle h(y) dy = f(x) dx,


$\displaystyle \int h(y) dy = \int f(x) dx.

This latter equation defines $ y$ implicitly as a function of $ x$, and in some cases it is possible to explicitly solve for $ y$ as a function of $ x$.

William Stein 2006-03-15