 Problem Statement

Solve the “Doomsday equation”
dN/dt = N^α
and show that for α > 1, the solutions approach a vertical asymptote in finite time. What happens for α < 1?
 Relevant Equations
 n/a
dN/dt = N^α
int(N^a)=int(dt)
[N^(1a)]/[1a]+c=t
I believe this is a solution, but it does not produce the results I am told to be looking for.
int(N^a)=int(dt)
[N^(1a)]/[1a]+c=t
I believe this is a solution, but it does not produce the results I am told to be looking for.