Question

y-y. Find all equilibrium points and check for sta- 3. Consider bility.

Answer 1

dy/dx = y - y^3 at equilibrium points dy/dx = 0 Rightarrow y - y^3 = 0 y(1 - y^2) = 0 Rightarrow y = 0, 1 or -1 dy/dx > 0 if y < -1 (try y = -2) (-2) - (-2)^3 = 6 dy/dx < 0 if -1 < y < 0 (try y = -0.5) dy/dx > 0 if 0 < y < 1 (try y = 0.5) dy/dx < 0 if y > 1 (try y = 2) 2 - 2^3 = -6 Phase line Solutions are converging near y = -1 or y = 1 hence the equilibrium points y = 1 and -1 are stable solutions are diverging near y = 0 hence y = 0 is unstable