Using (dot{x}=y), investigate the equation [ ddot{x}+left(x^{2}+dot{x}^{2}-1 ight) dot{x}+x=0 ] for how damping adds and removes energy

Using \(\dot{x}=y\), investigate the equation

\[ \ddot{x}+\left(x^{2}+\dot{x}^{2}-1\right) \dot{x}+x=0 \]

for how damping adds and removes energy from the system depending on the values of \(x\) and \(\dot{x}\).