Chapter 6, Problem 1PS

Doomsday Equation The differential equation

where k and e are positive constants, is called the doomsday equation.

(a) Solve the doomsday equation

$\frac{dy}{dt}=y^{1.01}$

given that $y(0)=1$. Find the time T at which

$\underset{t\to T}{\lim }y(t)=\infty$.

(b) Solve the doomsday equation

$\frac{dy}{dt}=k{y}^{1+e}$

given that $y(0)=y_0$.Explain why this equation is called the doomsday equation.