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

• To: mathgroup at smc.vnet.net
• Subject: [mg97856] Re: Question about how to graph the vector field for the differential
• From: Erik Max Francis <max at alcyone.com>
• Date: Tue, 24 Mar 2009 05:29:18 -0500 (EST)
• References: <gq7j9f\$qeo\$1@smc.vnet.net>

```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~!!

It's not clear what you're trying to accomplish.  Your differential
equation involves one function, y(x), and one independent variable, x.
This isn't a vector at all.  Written into Mathematica-speak:

In:= sol = DSolve[y'[x] == 2 x - y[x], y[x], x]

Out= {{y[x] -> 2 (-1 + x) + E^-x C}}

If you want to plot this, pull out the solution and play with it (%1 /.
sol[]).  If you want to graph it, just use Plot, but you'll have to
specify a value of the constant of integration C.

--
Erik Max Francis && max at alcyone.com && http://www.alcyone.com/max/
San Jose, CA, USA && 37 18 N 121 57 W && AIM, Y!M erikmaxfrancis
The only completely consistent people are the dead.
-- Aldous Huxley

```

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