1. The problem statement, all variables and given/known data Describe the phase portrait of the nonlinear system x' = x^2, y' = y^2 Also, find the equilibrium points and describe the behaviour of the associated linearized system. 3. The attempt at a solution We have an equilibrium point at (0,0). The associated linearized system is x' = 0, y' = 0. The phase portrait for this consists of lines of equilibria along x = 0, and y = 0. For the nonlinear system, I have found solutions x(t) = -1/t and y(t) = -1/t. I don't know what these solutions mean in terms of a phase portrait. Nor can I express the solutions in terms of constants x_0 and y_0.