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)
|
