Find all the equilibrium points of this second-order equation $x''+2x'=3x-x^3$ Find all the equilibrium points of this second-order equation $x''+2x'=3x-x^3$
I know that you must the roots of the equation, but when the equation isn't equal to $0$ I am confused on where to begin, thank you for any help!
edit: sorry, i did leave out a prime in there.  It is fixed now

You set $y=x'+2x$, then
$$
x'=y-2x\\
y'=3x-x^3
$$
and setting $x'=0=y'$ gives the stationary points.
