Can every differential equation be expressed in function notation?

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I often find differential equation written in function notation:

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I know it might be a trivial question,but....

Is this notation possible for every differential equation?

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Yes.

An equation is just a function of several variables $f(x,y,z,w,t,\cdots,k)$ set equal to zero, or even a constant.

For a differential equation, the variables include derivatives (partial or ordinary) of other variables.