It is an equation connecting a function with the independent variable, and its

own derivative (or derivatives) so a first order Ordinary Differential Equation

(ODE) is something like:

f(x, y, y')=0

a second order one is of the form:

f(x, y, y', y'')=0,

and so on for higher order.

A Partial Differential Equation (PDE) is similar but there are multiple

independent variables and also uses partial derivatives.

Some examples of ODEs:

1:

y'' = - 3 y,

or in standard form:

y'' + 3 y = 0.

2:

y'' + x y' + x^2 y = sin(3 x),

or in standard form:

y'' + x y' + x^2 y - sin(3 x) = 0.

RonL