Separable differential equation

Definition

The term separable is used for a first-order differential equation that, up to basic algebraic manipulation, is of the form:

${\frac {dy}{dx}}=f(x)g(y)$

It can be solved by rearranging and integrating:

$\int {\frac {dy}{g(y)}}=\int f(x)\,dx$

It suffices to have just one freely floating additive constant in the answer because the additive constants coming from the two integrals can be merged into one.