Order of Differential Equation/Warning

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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.