Solving for r in the Spruce Budworm project

[neldredge-unco]

odeproject-public/source/firstlook08.ptx

Lines 41 to 43 in f156486

	Solve the equation
	<me>rx(1-x) - \frac{x^2}{0.01 + x^2} = 0</me>
	and plot the result in the <m>xr</m>-plane for <m>0 \leq r \lt 1</m>.</p>

I don't think this step is really necessary to the problem. If the goal is to plot the bifurcation curve, we can just do it directly with Sage implicit_plot (or Desmos, etc) without needing to solve for one variable, nor reflect the curve as in the next step.

In fact, when I assigned this project, most students used implicit_plot to plot the reflected version anyway. But then they tended to think that the reflection was doing something mathematically very important, rather than just working around the restriction of only wanting to plot explicit functions, and so made an unnecessarily big deal about it.