Nonlinear Systems & Linearization · Superchallenge problem

The undamped pendulum $x' = y,\; y' = -\sin x$ is started at the bottom, $x(0) = 0$, with exactly the speed $y(0) = 2$ needed to creep up to the inverted position as $t \to \infty$. How long does it take to reach the horizontal position $x = \dfrac{\pi}{2}$? Give the exact value.