Are Both First and Second Derivatives Needed to Find Equilibrium Points in ODEs?

[cyt91]

Homework Statement

Find the equilibrium points for the following equation. Determine if the equilibrium points are stable and if stable,approximate the angular frequency.

(i) d2y/dx2 = cosh(x).

Homework Equations

The Attempt at a Solution

For equilibrium points, do we need to find dy/dx = 0 or d2y/dx2 = 0 or both?

Thank you.

 

[fauboca]

Homework Statement

Find the equilibrium points for the following equation. Determine if the equilibrium points are stable and if stable,approximate the angular frequency.

(i) d2y/dx2 = cosh(x).

For equilibrium points, do we need to find dy/dx = 0 or d2y/dx2 = 0 or both?

Thank you.

First derivative.