I believe that GenericThinker is interpreting ‘dy/dt = e^y’ as instructions to take the derivative of e^y (with respect to y or t I’m not sure). This is an extreme (and extremely arrogant) case of a general problem in lower-level and non-major math education; students learn to treat ‘=’ as a generic verb (although here it’s more of a preposition) instead of a symbol with a specific meaning. I work hard to beat this out of my algebra students, even though it usually won’t trip them up; but my calculus students (if they haven’t gotten it beaten out) do trip over it, much like GenericThinker is doing here.
I believe that GenericThinker is interpreting ‘dy/dt = e^y’ as instructions to take the derivative of e^y (with respect to y or t I’m not sure). This is an extreme (and extremely arrogant) case of a general problem in lower-level and non-major math education; students learn to treat ‘=’ as a generic verb (although here it’s more of a preposition) instead of a symbol with a specific meaning. I work hard to beat this out of my algebra students, even though it usually won’t trip them up; but my calculus students (if they haven’t gotten it beaten out) do trip over it, much like GenericThinker is doing here.