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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?

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3 Answers 3

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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 $y$).

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  • $\begingroup$ Ok, thanks for your detailed answer. $\endgroup$ Mar 28, 2013 at 23:44
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"Ordinary" is in contrast with "Partial" as is "Partial Differential Equations" or PDE

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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.

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