Drawing Direction Fields Online

Question

I am looking for a convenient and free online tool for plotting Direction Fields and Solution Curves of Ordinary Differential Equations. I tried the "Slope Field Plotter" on Geogebra; it worked tolerably well with direction fields, but for solution curves, some funny thing happens like this:

My Questions:

1. Why does the solution curve appear to be very different from circles?
2. Is there any alternative online free resources that will do a better job on this?

Edit:

I would love to use WolframaAlpha for this, if it works. Any suggestions on this?

Answer 1

You can use the command streamplot in wolframalpha like this:

streamplot[{1-x^2+y,1+x-y^2},{x,-3,3},{y,-3,3}]

where in the example above

$\dot{x}=1-x^2+y$ and $\dot{y}=1+x-y^2$

and the plot range is $x,y \in [-3,3]$