# Differential Equations

A differential equation is an equation that involves derivatives, or differentials. We previously look the differential equation of population growth. \[\frac{dP}{dt} = kP\] or \[P^\prime(t) = k \cdot P(t)\] where \(P\), or \(P(t)\) is the population at time \(t\). This equation is a model of uninhibited population growth. Its solution is the function \[P(t) = P_0e^{kt}\] where the constant \(P_0\) is the size of the population at \(t=0\). In general, differential equations have far reaching applications and have solutions that are functions. …