(* Tested on Mathematica version 10.2 and 11.3 *)
sol = NDSolve[{x'[t] == -y[t] - x[t]^2, y'[t] == 2 x[t] - y[t]^3,
z'[t] == 2 x[t] - z[t], x[0] == y[0] == z[0] == 1}, {x, y, z}, {t,10}];
Plot[Evaluate[{x[t], y[t], z[t]} /. sol], {t, 0, 10},
PlotLegends -> Placed[{"x[t]", "y[t]", "z[t]"}, Above]](*default colors*)
Plot[Evaluate[{x[t], y[t], z[t]} /. sol], {t, 0, 10}, PlotStyle -> {Red, Green, Blue},
PlotLegends -> Placed[{"x[t]", "y[t]", "z[t]"}, Above]]