I have the following 2-D dynamical system:
$\dot{y} = -y^2$, and $\dot{x} = y$
We can linearize the system, and find the eigenvectors that represent the manifolds. In this case, one of the eigenvectors is $(1,0)$ and the other is non-unique.
My question is: how can the manifolds be represented in equation form in this context? Or phrased differently, what are the equations of the (stable or unstable) manifolds?
Thank you