Question

For the autonomous first-order order differential equation dy=-18y+2y3, please 1. dx a. find its critical points; b. draw its phase portrait; c. clasify each critical point as asymptotcally stable, unstable, or semi-stable.

Answer 1

Given differential equation dy/dx = -18y + 2y^3 (a) Critical point dy/dx = 0 = > - 18y + 2y^3 = 0 2y(y^2 - 9) = 0 y 0, 3, - 3 critical point is y = 0, 3, - 3 (b) (c) y = 0 stable critical point y = -3 unstable critical point y = 3 unstable critical point.