consider the initial value problem

Here's the reasoning:

I had no idea so I consulted Wolfram|Alpha

http://www.wolframalpha.com/input/?i=y%27%3D4y%5E2

If you want an asymtote at t=7 then  

c1-4*7=0

c1=28

$$y(0)=\frac{1}{28-4*0}=\frac{1}{28}$$

I really am not sure that this is right.  I'm having a hard time getting my head around it.

thx a lot !