pr=ItoProcess[\[DifferentialD]x[t]==-((x[t])/(Sqrt[1+x[t]^2]))\[DifferentialD]t+Sin[x[t]]\[DifferentialD]w1[t]+Cos[x[t]]\[DifferentialD]w2[t],x[t],{x,0},t,{w1\[Distributed]WienerProcess[],w2\[Distributed]WienerProcess[]}]

paths=RandomFunction[pr,{0,4Pi,0.05},250,Method->"Milstein"]

ListLinePlot[paths["Part",1;;5]]

plot1=ListLinePlot[paths["Part",1;;12]];
plot2=DistributionChart[Transpose@(paths["SliceData",Range[0,4Pi,1.1]]),ChartStyle->Opacity[0.7]];
Show[plot1,plot2,PlotRange->{{0,11},Automatic}]

Show[plot1,plot2,PlotRange->{{0,11},Automatic},ImageSize->400,PlotLabel->Pane[Row[{HoldForm[\[DifferentialD]x[t]],"==",HoldForm[-((x[t])/(Sqrt[1+x[t]^2]))\[DifferentialD]t+Sin[x[t]]\[DifferentialD](Subscript[w, 1])[t]+Cos[x[t]]\[DifferentialD](Subscript[w, 2])[t]],", ",HoldForm[x[0]],"==",0}],400,Alignment->Center]]