# 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" (ODE) if the Ordinary part doesn't bring anything to it?

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 $y$).

• Ok, thanks for your detailed answer. Mar 28, 2013 at 23:44

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

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.