A linear ordinary differential equation of order is said to be homogeneous if it is of the form
(1)
|
where , i.e., if all the terms are proportional to a derivative of (or itself) and there is no term that contains a function of alone.
However, there is also another entirely different meaning for a first-order ordinary differential equation. Such an equation is said to be homogeneous if it can be written in the form
(2)
|
Such equations can be solved in closed form by the change of variables which transforms the equation into the separable equation
(3)
|