Rather bothered about constant of proportionality in differential equations

Could you please explain why when forming differential equations where the rate of change is negative i.e temperature loss, depreciating value, you would have to write things as dy/dt= -ky because 'k is a positive constant'- this is repeatedly emphasized in books.

Why can't you just do this: dy/dt= ky and simply state that k is negative?

Student X

You are not wrong in your assertion; that is if the problem has cited specific conditions for you to further solve for the value of the unknown constant. 

However, usually the minus sign is employed (ie letting k to be positive) because during instances when you are merely able to obtain the general solution, important exponential decay factors which contribute to stabilization of values in the long run (for example e^-kt) become more prominent/identifiable due to the minus sign showing up.

Hope this clarifies. Peace.

Best Regards,

Mr Koh