**Take $\ddot x = w-2x+x^2$, where $w\ge0$.
Show that the evolution of $x$ conserves a form of the energy and identify the potential function, sketching the phase portrait for $w=0$.**

I am not too sure what is meant by the question. I know that to prove energy is conserved, you need to show that the derivative equals $0$. If we take $V = w-2x+x^2$, then $\dot V = -2\dot x+2x\dot x = 2\dot x(x-1) = 0$, but how do we prove this equals $0$, if this is what we need to show?

I also thought it may be helpful to rewrite the equation as the system:
$\dot x=y$, $\dot y = w-2x+x^2$, which would give $\dot V = 2y(x-1)$.

Any help would be hugely appreciated, thank you!