Hi, I found the same problem I needed a help to solve somewhere in this forum. However, I could not reach the answers only with the help provided on that page. I would really appreciate it if someone could offer me some help.(adsbygoogle = window.adsbygoogle || []).push({});

P: Let c be a positive number. A differential equation of the form: dy/dt = ky^(1+c)

where k is a positive constant, is called a doomsday equation because the equation in the expression ky^(1+c) is larger than that for natural growth (that is, ky).

(a) Determine the solution that satisfies the initial condition y(0)=y(subzero)

What I did was

dy/y^-(1+c)=k dt Integrate both sides I got

y(t)=1/[ck(T-t)]^(1/c) for some constant T

Is this correct?

(ba) Show that there is a finite time t = ta (doomsday) such that lim(t->T-) wy(t) = infinity

For the equation, infinity = (limt->T-)1/[ck(T-t)]^1/c, when t approaches to T, T=t or T-t=0, which makes the denominator 0, hence the value of the equation becomes infinity.

Is this what I need to say, or should I get the exact value of t (can I?)???

(c) An especially prolific breed of rabbits has the growth term ky^(1.01). If 2 such rabbits breed initially and the warren has 16 rabbits after three months, then when is doomsday?

Since y^(1.01), c=0.1. and Y(3)=16, By substituting those numbers to the equation to obtain the value of k.

16^0.1=1/[0.1*k(3)]^(1/0.1)

[0.3k]^10=1/1.32

0.3k=(1/1.32)^(1/10)

k=0.9726

This time use wy(0)=2 to get the value of T

2=1/[0.1*0.9726*T]^(1/10)

[0.1*0.9726*T]^(1/10)=1/2

[0.1*0.9726*T]=(1/2)^(1/10)

T=0.9330/0.09726=(approx)9.6months

How does that sound?

I have no confident with these solutions, especially (c).

Someone, please help me!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Doomsday Equations

**Physics Forums | Science Articles, Homework Help, Discussion**