Your question is not clear. But here is a starting for you.

Just adopting [Chris answer][1] to same sort of question,

    Eq1 = x'[t] == x[t]^2 + 2*y[t];
    Eq2 = y'[t] == 3*x[t];
    splot = StreamPlot[{x^2 + 2*y, 3*x}, {x, -6, 6}, {y, -6, 6}, 
      StreamColorFunction -> "Rainbow"]
    Manipulate[
     Show[splot, 
      ParametricPlot[
       Evaluate[
        First[{x[t], y[t]} /. 
          NDSolve[{Eq1, Eq2, Thread[{x[0], y[0]} == point]}, {x, y}, {t, 
            0, T}]]], {t, 0, T}, PlotStyle -> Red]], {{T, 1}, 0.1, 
      1}, {{point, {0.01, 0.0}}, Locator}, SaveDefinitions -> True]

[![enter image description here][2]][2]


  [1]: http://mathematica.stackexchange.com/questions/14160/plotting-a-phase-portrait?rq=1
  [2]: https://i.sstatic.net/XzP0H.png