RE: direction fields for diff eqns in mathematica 3.0?

*To*: mathgroup at smc.vnet.net*Subject*: [mg25023] RE: [mg25018] direction fields for diff eqns in mathematica 3.0?*From*: "David Park" <djmp at earthlink.net>*Date*: Fri, 1 Sep 2000 21:57:30 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Here is a simple differential equation: y'[x] == y[x]^2 A direction field vector would be given by: v = {1, y^2} To plot the direction field I found it easiest to normalize the vector. v/Sqrt[v.v] {1/Sqrt[1 + y^4], y^2/Sqrt[1 + y^4]} This plots the direction field. Needs["Graphics`PlotField`"] Needs["Graphics`Colors`"] PlotVectorField[{1, y^2}/Sqrt[1 + y^4], {x, -3, 3}, {y, -7, 7}, ScaleFunction -> None, HeadLength -> 0, AspectRatio -> 1, PlotRange -> {{-4, 4}, {-10, 10}}, Background -> Linen, Frame -> True, FrameLabel -> {x, y}, PlotLabel -> Derivative[1][y][x] == y[x]^2, ImageSize -> 600]; The plots usually look a little nicer if you make the PlotRange somewhat larger than the iterator range; otherwise some of the lines may overshoot the frame. David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ > -----Original Message----- > From: Ed [mailto:ejh at idcomm.com] To: mathgroup at smc.vnet.net > > Howdy all! > > I cannot find a simple way to do direction field plots for > differential equations. I mean the plots which show the slope of the > solutions curves at each point. > > What am I missing? Do I use something fancy with the vector plot > functions? > > Thanks! > > Ed