Searching for some help with trying to sketch the phase portrait for the system,
$$\ddot{x}=ax-x^2$$
for values of $a=0$, $a<0$, $a>0$.
How can I set up the Jacobian matrices and sketch the phase portrait of this system?
$\dot{x}=y$
$\dot{y}=ax-x^2$
then,
$y=0$
$x=0$
$x=a$