To start with, we calculate the steady states, i.e.:
Thus the steady states are y = 0 , y = a {\displaystyle \displaystyle y=0,\,y=a} .
The initial condition is y ( 0 ) = 2 a , a > 0 {\displaystyle y(0)=2a,\,a>0} , which is above y = a {\displaystyle \displaystyle y=a} . Since d y d t | t = 0 = ( y ( 0 ) ) 2 ( y ( 0 ) − a ) = ( 2 a ) 2 ( 2 a − a ) > 0 {\displaystyle \left.{\frac {dy}{dt}}\right|_{t=0}=(y(0))^{2}(y(0)-a)=(2a)^{2}(2a-a)>0} , the solution is increasing away from the steady state y = a {\displaystyle \displaystyle y=a} to infinity:
In other words, lim t → ∞ y ( t ) = ∞ {\displaystyle \lim _{t\to \infty }y(t)=\infty } , which is answer (B) {\displaystyle {\color {blue}{\text{(B)}}}} .
.
, which is above 
. Since 
, the solution is increasing away from the steady state to infinity:
, which is answer 
.
