numerical integration – How add noise to a differential equation?

I have a differential equation:

$$frac{dx}{dt}=sech(x-1)$$

I want to add noise to it and try to solve it numerically, but it seems that I am programming something wrong, because there is no noise. I am trying to do this by adding a random number.

``````ClearAll("Global`*")

pars = {(Alpha) = 1, (Beta) = 1/20, (Gamma) = 1,
h = 1, (Omega) = 2 Pi 1/2, (Mu) = 1, xs = -1, xe = 1}

f = Sech(x(t) - xe)

sys = NDSolve({x'(t) ==
ArcTan(1 D(f, x(t))) + RandomReal({-1/10, 1/10}),
x(0) == xs}, {x}, {t, 0, 500})

Plot({Evaluate(x(t) /. sys), xe}, {t, 0, 10}, PlotRange -> All,
PlotPoints -> 40)
``````