Re: graphing implicit function

*To*: mathgroup at smc.vnet.net*Subject*: [mg14244] Re: graphing implicit function*From*: Paul Abbott <paul at physics.uwa.edu.au>*Date*: Mon, 12 Oct 1998 13:51:29 -0400*Organization*: University of Western Australia*References*: <6vf60d$dil@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

David Ridley wrote: > I have a differential equation about which I'm trying to get some > intuition. > > y'[x] = 1/2 + ((1-Z)(A-2x+B) / 2Z(A-2x+y[x])) > > I'd like to be able to graph it. Some comments: [1] Writing your differential equation as de = y'[x] == ((a + b - 2*x)*(1 - z))/(2*z*(a - 2*x + y[x])) + 1/2; DSolve can go some way towards solving this, i.e., DSolve[de, y[x], x] [2] For fixed a, b, and z, you can use NDSolve: NDSolve[{de /. {a->1, b->1, z->1/2}, y[0] == 5}, y, {x, 0, 3}]; and then Plot[Evaluate[y[x] /. %], {x, 0, 3}]; > I used a linear transformation and then integrated over X to obtain: > > Y = 2 X Log[Y] / (4 Z Log [Y] - (1-Z) Log [2 X]) > > Is it possible to graph an implicit function like this using > Mathematica? You can use ImplicitPlot in Graphics`Graphics`. Alternatively, you can use ContourPlot for fixed z, e.g., ContourPlot[Evaluate[y - (2*x*Log[y])/(4*z*Log[y] - (1 - z)*Log[2*x]) /. z -> 1/2], {x, 0.1, 4}, {y, 0.1, 4}, Contours -> {0}, PlotPoints -> 200, ContourShading -> None]; or ContourPlot3D (also in Graphics`Graphics`). Cheers, Paul ____________________________________________________________________ Paul Abbott Phone: +61-8-9380-2734 Department of Physics Fax: +61-8-9380-1014 The University of Western Australia Nedlands WA 6907 mailto:paul at physics.uwa.edu.au AUSTRALIA http://www.physics.uwa.edu.au/~paul God IS a weakly left-handed dice player ____________________________________________________________________