Diff Equation: dP − kP dt = 0 Initial Condition P(0) = P0

Question

Its on web assign, I need help

Answer 1

dP = kPdt

(1/P)dP = kdt

∫(1/P)dP = ∫kdt

ln l P l = kt + C

l P l = e^{kt + C} = e^Ce^kt

P(t) = ±e^Ce^kt

Relabel ±e^C as C to get P(t) = Ce^kt

Since P(0) = P_0, P(t) = P₀e^kt.