SetDirectory["C:\\drorbn\\AcademicPensieve\\Classes\\12-267"]

p=(x^3)-3x (y^2);quad=Expand[{D[p,y], -D[p,x]}/3]

VectorPlot[quad, {x,-1,1}, {y,-1,1}]

MakeImage["MonkeySaddleFlow",
Show[Join[
{VectorPlot[quad, {x,-1,1}, {y,-1,1}, Frame->None]},
Table[
eqns=Join[
Thread[{x'[t], y'[t]} == (quad /. {x->x[t], y->y[t]})],
{x[0]==RandomReal[{-1,1}], y[0]==RandomReal[{-1,1}]}
];
sol=NDSolve[eqns, {x,y}, {t,-1,1}];
ParametricPlot[
Evaluate[{x[t], y[t]} /. sol],
{t,-1,1},
PlotRange -> {{-1,1},{-1,1}}, ColorFunction -> (Red&)
],
{100}
]
]]
]