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ODE's are equations containing a function of one independent variable and its derivatives.

The term "ordinary" just means the subject excludes the use of partial derivatives.

Basically, they are equations in which specific variables will be expressed as a derivative. They are used to denote the change of variables relative to the change of other variables.

With an equation like y=mx+b you can write it as a differential equation by putting:

y = (dy/dx)x + b

but it is hardly necessary to do so because it is easy to solve.

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