calc.."doomsday equation" help plz..?

Question

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 exponent 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_0.
b) Show that there is a finite time t =T (doomsday) such that lim t->T- y(t) = infinity
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?

show work/steps plz..thanks!

Answer 1

The integral of y^(-1-c)dy = the integral of kdt

So y^(-c)/(-c) = kt + constant.

Rearrange terms to get y as a function of t and proceed from there.