Q:

Choose the correct graph of solution curve from the following options:

Use the qualitative theory of Autonomous differential equations to sketch the graph of the solution of 
$ y'=y(y-7)(y+7) , \\ y(0)=-9, \ y(0)=-1, \ y(0)=6, \ y(0)=8 \ $
Choose the correct graph of solution curve from the following options:

Answer:
The differential equation is 
$ y'=y(y-7)(y+7) \ $
The equilibrium points are given by 
$ y=0, \ 7 , \ -7 \ $
Also,
$ y'>0 \ $ on  the  interval $ \ (7,\infty) \ $
$ y'<0 \ $ on  the  interval $ \ (0,7) \ $
$ y'>0 \ $ on  the  interval $ \ (-7,0) \ $
$ y'<0 \ $ on  the  interval $ \ (-\infty,-7) \ $
Thus option $ \ (A) \ $ and $ \ (B) \ $ seems to be correct.
But which one should be answer?
I think the initial conditions need to apply now.
But I am unable to do it.
Help me finishing the answer.

A:

The only correct solution is $A.$
$B$ is decreasing on $(-7,0)$ which is contradictory to the given equation.  

