general solution of a differential equation in explicit form

Question

I need to find the general solution of a differential equation in explicit form

$$\dfrac {dp}{dh} = -Kp$$

My solution: I used the separation of variables and after doing the integrations I obtained $\ln p = -Kh + c$

The general solution in explicit form, by an index law I obtained $$p = e^c e^{-Kh}$$ $$p = Ae^{-Kh}$$

Is my working correct, please?

Answer 1

Yes, your solution is correct.

Answer 2

No, the derivation is not quite correct. What if $p=0$ or $p<0$?