Separable ODEs

#todo Generalise to N-order ODEs.

A separable first order ODE is a differential equation consisting of variables that can be separated using Integration By Substitution.

They are of the form:

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

And can be separated as such:

$\frac{1}{g(y)}\times \frac{dy}{dx}=f(x)$ $⟹\int \frac{1}{g(y)}\frac{dy}{\cancel{dx}}\cancel{dx}=\int f(x)dx$ $⟹\int \frac{1}{g(y)}dy=\int f(x)dx$