In Problems 9 through 12, find each equilibrium solution x(t) x 0 of the given second-order differential equation x + f(x , x') =

In Problems 9 through 12, find each equilibrium solution x(t) Ξ x₀ of the given second-order differential equation x" + f(x , x') = 0. Use a computer system or graphing calculator to construct a phase portrait and direction field for the equivalent first-order system x' = y, y' = -f(x , y). Thereby ascertain whether the critical point (x₀, 0) looks like a center, a saddle point, or a spiral point of this system.

x" + (x² - 1)x' + x = 0