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)=128−4∗0=128
I really am not sure that this is right. I'm having a hard time getting my head around it.