Q:

Non-ordinary differential equation?

Does such a thing exist ?
Can't seem to find anything about it so i was wondering : why bother calling something "Ordinary Differential Equation" if the "Ordinary" part doesn't bring anything to it ?

A:

It's called an "ordinary differential equation" because it involves a function (or functions) of one independent variable and normal (i.e. not partial) derivatives, whereas a "partial differential equation" involves functions of multiple independent variables and partial derivatives.
For example,
$$
y' + 2xy = 3x
$$
is an ordinary differential equation (the independent variable being x), and
$$
\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = 0
$$
is a partial differential equation (the multiple independent variables being $x$ and $y$).

A:

"Ordinary" is in contrast with "Partial" as is "Partial Differential Equations" or PDE

A:

In addition to what others have already said, there are other types of differential equation.
There's the Stochastic Differential Equation, which contain random elements.
There's the Differential-difference equation, which is a blending of differential and difference equations, such as
$$
\frac{d}{dx}f(x)=f(x-1)
$$
So an ordinary differential equation is a differential equation that doesn't have anything "special" about it, it's just a differential equation. It is, quite literally, ordinary.

