Population $\dot x = x (1-x)$

Show[Table[
Plot[Evaluate[x[t]/.NDSolve[{x'[t] == x[t](1-x[t]), x[0] == x0}, x,
{t, 0, 3}]],{t,0,3},PlotRange->{{0,3},{0,4}},Frame->True],{x0,0,4,.25}]]