Order of Differential Equation/Warning

Warning on Order of Differential Equation
Consider the ordinary differential equation:


 * $y - y + y' - y = 0$

At first glance it looks as though it is of the $2$nd order.

But after some (fairly obvious) simplification, it is seen that it can be written:


 * $y' - y = 0$

which is of the $1$st order.