1. The problem statement, all variables and given/known data x'=x(x^2+y^2) y'=y(x^2+y^2) 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? 2. Relevant equations 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.