# Doomsday Equation

by noboost4you
Tags: doomsday, equation
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,503 How much of hint do you need? That's a separable equation (that's what cookiemonster was telling you) and can be written as $$\frac{dy}{y^{1+c}}= kdt$$ which can be integrated. By the way it's called the "doomsday" equation not just "because the equation in the expression ky^(1+c) is larger than that for natural growth (that is, ky)" but because there is a singularity: at some finite time (t= y0/(ck)) the population goes to infinity: "doomsday".