Find the critical points and phase portrait of the given aut

Find the critical points and phase portrait of the given autonomous first-order differential equation. Classify each point as asymptotically stable, unstable, or semi-stable. dy/dx = y^3 - 4y Select all correct answers. Select one or more: a. 2, unstable b. 0. stable c. -2, unstable d. 4. stable e. -4. unstable f. semi-stable g. 2, stable h. -2, semi-stable

Solution

Given that

dy/dx = y³ - 4y

Set dy/dx = 0 for finding critical points

y³ - 4y = 0

y ( y² - 4 ) = 0

y ( y + 2 ) ( y - 2 ) = 0

y = 0 , -2 , 2

Therefore ,

Critical points are -2 , 0 , 2