Re: directionfields from StreamPlot looks different from

*To*: mathgroup at smc.vnet.net*Subject*: [mg100468] Re: [mg100444] directionfields from StreamPlot looks different from*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Fri, 5 Jun 2009 03:00:36 -0400 (EDT)*Organization*: Mathematics & Statistics, Univ. of Mass./Amherst*References*: <200906040732.DAA11830@smc.vnet.net>*Reply-to*: murray at math.umass.edu

You're not. For the "direction field" of a 1-dimensional ordinary differential equation y' == f[t, y], the vector field you want to plot is {1, f[t,y]}. So... streams = StreamPlot[{1, t^2 - y}, {t, -4, 4}, {y, -2, 10}, StreamStyle -> Directive[Orange]]; sol = Table[NDSolve[{y'[t] == t^2 - y[t], y[0] == y0}, y[t], {t, -4, 4}], {y0, 0, 6, 0.5}]; solutionCurves = Plot[y[t] /. sol, {t, -4, 4}, PlotRange -> {{-4, 4}, {-2, 10}}]; Show[{solutionCurves, streams} Note that you do not need any parentheses around t^2. And in the current version of Mathematica, you no longer need to wrap y[t]/.sol with Evaluate -- unless you would like the curves automatically to be given different colors. sean_incali at yahoo.com wrote: > I don't think I'm using StreamPlot properly. > > Consider the following non-autonomous ODE > > y'[t] == (t^2) - y[t] > > Solutions for various ICs can be viewed by the following. > > sol= Table[NDSolve[{y'[t] == (t^2) - y[t], y[0] == y0}, y[t], {t, -4, > 4}], {y0, 0, 6, 0.5}]; > > Plot[Evaluate[y[t] /. sol], {t, -4, 4}, PlotRange -> {{-4, 4}, {-2, > 10}}] > > Shouldn't Vector fields be similar to the solutions above? If I plot t > on x-axis vs. t^2-y on y axis... > > VectorPlot[{t, (t^2) - y}, {t, -4, 4}, {y, -2, 10}] > > StreamPlot[{t, (t^2) - y}, {t, -4, 4}, {y, -2, 10}] > > I don't get similar results... > > What is the reason for this? > > Thanks much in advance > > Sean > > > > -- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305

**References**:**directionfields from StreamPlot looks different from solution***From:*sean_incali@yahoo.com