Chapter 5.1, Problem 1E

Consider the three systems

(i) $\frac{dx}{dt}=2x+y$ (ii) $\frac{dx}{dt}=2x+y$ (iii) $\frac{dx}{dt}=2x+y$

$\frac{dy}{dt}=-y+x^2\frac{dy}{dt}=y+x^2\frac{dy}{dt}=-y-x^2$

All three have an equilibrium point at $(0,0).$ Which two systems have phase portraits with the same "local picture" near (0, 0)? Justify your answer. [Hint: Very little computation is required for this exercise, but be sure to give a complete justification. ]