Hi there,
it would have helped to have the actual ODE, but I will for this illustration just make one up:
eqL\[Gamma] = \[Gamma]''[t] - \[Gamma]'[t] - \[Gamma][t] == Sin[t];
You can then run your NDSolve
s = NDSolve[{eqL\[Gamma], \[Gamma][0] == .79, \[Gamma]'[0] == 0}, \[Gamma][t], {t, 0, 2}]
Then you can define the x[t]; note that you need to add values for
$l$ and
$r$ unless you want to use Manipulate or Animate.
x = 1/2 (2 r Cos[\[Gamma][t]] + Sqrt[2] Sqrt[2 l^2 - r^2 + r^2 Cos[2 \[Gamma][t]]]) /. {s[[1, 1]], r -> 1, l -> 1}
and plot
Plot[x, {t, 0, 3}]
Cheers,
M.