The document discusses a phase plot of an autonomous ordinary differential equation (ODE) and outlines three tasks: identifying and classifying equilibrium points, determining the limit of a solution at a specific initial condition, and assessing the existence of a solution that meets given initial values. It focuses on stability classifications such as stable, unstable, and semi-stable for equilibrium points. Additionally, it poses a true or false question regarding the uniqueness of solutions for specific initial conditions.

1. The phase plot of an autonomous ODE is given by this graph 1. Find the euqilibrium and
classify them: stable, unstable, semi-stable. 2. If y is a solution such that y(0)=5, Find tlimy(t) 3.
True or False: there exists a solution such that y(0)=1 and y(1)=1