Show that the Euler-Lagrange equation for the functional
$S[y] = \int_0^{\frac{\pi}{6}} (y'^2 - 9y^2 + 20 \sinh(x) y) \, dx$, $y(0) = 1$, $y(\frac{\pi}{6}) = 0$,
is
y'' + 9y = 10 \sinh(x).
Show that the stationary function is given by
y = \cos(3x) - \sinh(\frac{\pi}{6}) \sin(3x) + \sinh(x).
