Try a numerical solution with two initial conditions to accommodate the second order. In Mathematica I was able to solve as follows.
Clear["Global`*"];
NDSolve[
{x''[t] + 9 x[t] - Sin[x[t]] == 0, (*Two initial conditions.*)x[0] == 1, x'[0] == -1},
x[t], {t, -2 Pi, 2 Pi}]
Plot[x[t] /. %, {t, -2 Pi, 2 Pi}]