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)
(b) Show that there is a finite time t = ta (doomsday) such that lim(t->T-) wy(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?
First i wanted to find solution to the dy/dx (meaning i integrated it)
I got y^c = -c(kx+T)
but i could not define it as function y because of the negative sign in front of C
does it always have to be function y of c ? can we just leave it at that?
What should i do?