Find all equilibrium points of the given system and determine whether we have linear stability at them or not. (please answer both showing your work)

(i) x ′ = x^(2)+ y^(2) − 1

y ′ = x − y

(ii) x ′ = 1 − e^(y)

y ′ = 1 − x^(2) − x sin(y)

Answer rating: 100% (QA)

To find the equilibrium points of the given system we set the derivatives equal to zero and solve for x and y i x x2 y2 1 0 y x y 0 From the second equation we have x y Substituting this into the firs... View the full answer