# Plotting simple ODE system phase portrait [duplicate]

I have the following system of equations:

\begin{cases} \dot x = 2xy \\ \dot y = 1 - x^2 - y^2 \end{cases}

What I want is to draw the phase portrait in the rectangle $[-4,4]\times[-4,4]$. This looks like the most natural thing one want to do as long as he wants to study phase portraits, since drawing them manually will take a lot of time. Unfortunately I was not able to find Mathematica code and since I am newbie I can not write it myself. I am sure this type of question is relevant for all ODE students, but I was not able to find the answer here.

## marked as duplicate by C. E., m_goldberg plotting StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); May 27 '17 at 15:17

I suggest, you study the documentation about StreamPlot.

StreamPlot[{2 x*y, 1 - x^2 - y^2}, {x, -4, 4}, {y, -4, 4}]


Explanation:

{2 x*y, 1 - x^2 - y^2}


{x, -4, 4}


Is the range for your x-coord. (from -4 to 4)

{y, -4, 4}


vice versa with y.

Perhaps also interesting: LineIntegralConvolutionPlot

Related

Hope this helps.