Question

dp dt= -2p. p(0)= 1

Answer 1

Quisiste decir  
                               $\dfrac{dp}{dt}=-2p$

$\displaystyle dt = -\dfrac{dp}{2p}\\ \\ \int dt=-\int \dfrac{dp}{2p}\\ \\ t=-\dfrac{1}{2}\ln p+C\\ \\ 0=-\dfrac{1}{2}\ln 1+C\\ \\ C=0\\ \\ t=-\dfrac{1}{2}\ln p\\ \\ \boxed{p=e^{-2t}}$