Question

(1 point) Find the equilibrium points of dy-e o. 7 and classify each one as stable or unstable. Stable equilibria occur at y- Unstable equilibria occur at y (If there is more than one equilibrium of a certain type, enter a comma-separated list. If there are no equilibria, enter "none")

Answer 1

Dy/dx = e^-64 -7 put dy/dt = 0 implies e^-64 -7 = 0 implies e^-64 = 7 implies -64 = ln(7) implies y = -1/6 ln(7) Now dy/dx < 0 for y > -1/6 ln (7) and dy/dt > 0 for y < -1/6 ln (7) implies dy/dt changes sign from positive to negative as y increases implies y = -1/6 ln (7) is stable hence stable equilibria occur at y = -1/6 ln (7) unstable equilibria occur at y = none]