$\dot x = \sin x$

Show[Table[
Plot[Evaluate[x[t]/.NDSolve[{x'[t] == Sin[x[t]], x[0] == x0}, x,
{t, 0, 3}]],{t,0,3},PlotRange->{{0,3},{-10,10}},Frame->True],{x0,-3Pi,3Pi,.5}]]