Author 
Comment/Response 
Bill Simpson

11/20/12 6:26pm
In Response To 'Re: Re: DSOLVE not computing'  Since you didn't provide any initial conditions or or the range of t or hints about how fine grained you want your phase plot to be I will have to guess a bit here.
See if you can understand and adapt this to your needs.
In[1]:= Show[Table[{f,g} = {x[t],y[t]} /. NDSolve[{x'[t]==x[t](22x[t]y[t]), y'[t]==(3x[t]3 y[t])y[t], x[0]==i, y[0]==j}, {x,y}, {t,0,10}][[1]];
ParametricPlot[{f,g}, {t,0,10}],
{i,1,2,1/3}, {j,1,2,1/2}]]
Out[1]= <graphic snipped>
What that does is create a Table of solutions and plots, one for each {x[0],y[0]}={i,j}, and then combines all those into a single phase portrait graphic.
Test this carefully, perhaps starting with a much simpler set of equations where you know exactly what the portrait should be, and make certain it is correct before you depend on this.
If this is not what you were looking for and you can provide some more information then perhaps someone can come up with a way to get what you need.
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