I have Hamiltonian system $$ \begin{align} \dfrac {dx}{dt}=&y \\ \dfrac {dy}{dt}=&5x^2+3x+7 \end{align} $$ I have found Hamiltonian which is $$H(x,y)=-\dfrac {5x^3}3-\dfrac {3x^2}2+7x$$ I calculated the equilibrium points to be $(-1.52,0)$ and $(0.92,0)$ And I built phase plane
But I don’t understand what kind of phase plane is it. Is it a node? Center? Spiral?
