if the definition of a "linear" equation seems arbitrary, it's because the
definition *is* arbitrary.  in mathematics, the person making the definition is
the one making the rules.  however you want to define a term, you may.

however...

the definition of "linear" is arbitrary but it *is not* capricious.  you may
make any definition you want of a term in mathematics.  the key test is whether
or not the definition is *useful*.  (it helps if the term is descriptive too,
among other things, but that's another story.)

in this case, our definition of linear allows our method for solving first order
linear equations to work the way it does (and solve as many equations as it does
- we *don't* need "t" to appear in a linear fashion, just "y").  we're also
seeing now that linearity - as we've defined it - allows us to use the principle
of superposition.