Mathematica Constructing Phase Portrait of System with Mathematica

[ManuelF]

How can I construct the phase portrait(with Mathematica) of the following system?
\dot{x}(t)=y(t)
\dot{y}(t)=-x^3(t)+4x(t)y(t)

 

[Dale]

The phase portrait would be four dimensional, so it would be pretty hard to plot.

 

[Dale]

Oops, my previous response was incorrect. I didn't notice that this is two first order equations instead of two second order equations. The phase portrait can be easily obtained as:

StreamDensityPlot[{y, -x^3 + 4 x y}, {x, -1, 1}, {y, -1, 1}]