Slope Field Plotting I am trying to compute the slope field for $\frac{dy}{dx}=(-.5y+.0001yx)/(2x(1-.0001x)-.01xy)$. My graphing calculator and software like wolfram alpha seem inadequate to get a useful view. Does anyone have any recommendations as far as tools that can handle this equation?
If you want to post a screen shot and provide hints I would work to recreate your answer as well.
 A: As far as tools, you can look into things like Mathematica, Maple, Matlab (these are professional packages and are not free). If you are looking for free tools, you can consider such things as Maxima, SAGE or Octave. You can also try a Java app called DFIELD.
Here are some items for you to consider as an analytical approach:


*

*What happens at $y = 0$ to the slope $\dfrac {dy}{dx}$?

*What happens for very small values of $y$?

*Create a table for two sets of points in each quadrant and calculate $\dfrac {dy}{dx}$. What do you notice about the slope in each of those quadrants?

*Some mildly interesting things happen for larger $x$ and $y$ values in the first quadrant, so do some analysis to see where those occur.


There are some other things you can do analytically and you can also solve this numerically and draw solution curves.
Putting this all together (you should really try all of these things), you would "manually" get the Direction Field Plot:

Here is a second DF Plot for a range you were interested in.

