i) Find all the equilibrium points and describe the behavior of the associated linearized system
ii) Describe the phase portrait for the nonlinear system
iii) Does the linearized system accurately describe the local behavior near the equilibrium points?
Solving for equilibrium, you get: x=0 and x^2+y^2=0. Likewise with second function, you get: y=0 and x^2+y^2=0. But I don't know what the phase portrait will behave.