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Re: Question about how to graph the vector field for the

  • To: mathgroup at smc.vnet.net
  • Subject: [mg97885] Re: [mg97836] Question about how to graph the vector field for the
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Tue, 24 Mar 2009 05:34:48 -0500 (EST)
  • Reply-to: hanlonr at cox.net

Clear[y]

y[c_][x_] =
  y[x] /.
    DSolve[y'[x] == 2 x - y[x], y[x], x][[1]] /.
   C[1] :> c

c E^-x+2 (x-1)

D[y[c][x], x] == 2 x - y[c][x] // Simplify

True

Plot[
  Evaluate[
   Table[
    Tooltip[y[c][x]],
    {c, -3, 5}]],
  {x, -1/2, 3}]

Plot3D[y[c][x], {x, -1/2, 3}, {c, -3, 5}]

Manipulate[
  Plot[y[c][x], {x, -1/2, 3},
   PlotRange -> {-8, 5}],
  {c, -3, 5}]



Bob Hanlon


On Mon, Mar 23, 2009 at 7:35 AM , jo1e984 at gmail.com wrote:

> i need to graph the vector field and the family of solutions for the
> DE: dy/dx=2x-y
> and i tried the graph the vector field, but while i tried to use the
> VectorFieldPlot it show up some kind of wierd graph...
> and i cannot even get start on the "family of Solutions"
> graph...searched online but still cannot figure out.
> hope some pros can help me out on this...thx alot~!!
> Bluefly


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