So I have the system
\begin{align} x'&=y\\ y'&=-x-y\ln(x^2+4y^2) \end{align} To find the equilibrium points I need $x'=0$ and $y'=0$, thus I obtain
\begin{align} y&=0\\ -x-y\ln(x^2+4y^2)&=0 \end{align}
I don't see how to proceed here. If $y=0$ in the second equation we get $-x=0\Leftrightarrow x=0$ but if $x=0$ and $y=0$ the logarithm is undefined. So $(0,0)$ can't be an equilibrium point.
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